saturate(...,Strategy=>...)

Description

There are four strategy values:

Iterate

saturate(I,J,Strategy => Iterate) -- indicates that successive ideal or module quotients should be used.

This value is the default.

Linear

saturate(I,J,Strategy => Linear)Strategy => Linear -- indicates that the reverse lex order should be used to compute the saturation.

This presumes that J is a single, linear polynomial, and that I is homogeneous.

Bayer

saturate(I,f,Strategy => Bayer) -- indicates that the method of Bayer's thesis should be used.

The method is to compute (I:f) for I and f homogeneous, add a new variable z, compute a Gröbner basis of (I,f-z) in reverse lex order, divide by z, and finally replace z by f.

Eliminate

saturate(I,f,Strategy => Eliminate) -- indicates that the saturation (I:f) should be computed by eliminating fz from (I,f*z-1), where z is a new variable.

Functions with optional argument named Strategy:

addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
annihilator(...,Strategy=>...) -- see annihilator -- the annihilator ideal
basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
mingens(...,Strategy=>...) -- see Complement -- a Strategy option value
trim(...,Strategy=>...) -- see Complement -- a Strategy option value
compose(Module,Module,Module,Strategy=>...) -- see compose -- composition as a pairing on Hom-modules
decompose(Ideal,Strategy=>...) (missing documentation)
determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
dual(MonomialIdeal,List,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
dual(MonomialIdeal,RingElement,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
dual(MonomialIdeal,Strategy=>...)
End(...,Strategy=>...) -- see End -- module of endomorphisms
exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
gb(...,Strategy=>...) -- see gb -- compute a Gröbner basis
GF(...,Strategy=>...) -- see GF -- make a finite field
groebnerBasis(...,Strategy=>...) -- see groebnerBasis -- Gröbner basis, as a matrix
Hom(...,Strategy=>...) -- see Hom -- module of homomorphisms
homomorphism'(...,Strategy=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
hooks(...,Strategy=>...) -- see hooks -- list hooks attached to a key
intersect(Ideal,Ideal,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Module,Module,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
isPrime(Ideal,Strategy=>...) (missing documentation)
match(...,Strategy=>...) -- see match -- regular expression matching
minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
normalCone(Ideal,RingElement,Strategy=>...) (missing documentation)
normalCone(Ideal,Strategy=>...) (missing documentation)
parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
pushForward(...,Strategy=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
quotient'(...,Strategy=>...) (missing documentation)
quotient(...,Strategy=>...)
resolution(...,Strategy=>...)
saturate(...,Strategy=>...)
syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

Default value: null
Function: saturate -- saturation of ideal or submodule
Option key: Strategy -- an optional argument

The source of this document is in Saturation/saturate-doc.m2:139:0.