localModulo -- find the pre-image (pullback) of image of a map over a local ring

Synopsis

• Usage:

  localModulo(m,n)

• Inputs:
  • m, a matrix
  • n, a matrix
• Outputs:
  • a matrix, whose image is the pre-image (pullback) of the image of n under m

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : setMaxIdeal ideal vars R

o2 = ideal (x, y, z)

o2 : Ideal of R

i3 : m = matrix {{x-1, y}}

o3 = | x-1 y |

             1      2
o3 : Matrix R  <-- R

i4 : n = matrix {{y,z}}

o4 = | y z |

             1      2
o4 : Matrix R  <-- R

i5 : modulo (m,n)

o5 = {1} | 0  z 0 y    |
     {1} | -1 0 z -x+1 |

             2      4
o5 : Matrix R  <-- R

i6 : localModulo (m,n)

o6 = {1} | z y    0  |
     {1} | 0 -x+1 -1 |

             2      3
o6 : Matrix R  <-- R

See also

• setMaxIdeal -- set the maximal ideal for local ring methods
• localComplement -- find the splitting of the target of a map
• localsyz -- find syzygies
• localMingens -- finds a minimal set of generators
• localPrune -- find a minimal presentation
• localResolution -- find a resolution over a local ring
• residueMap -- The class of all local rings
• maxIdeal -- The class of all local rings