localComplement -- find the splitting of the target of a map

Synopsis

• Usage:

  localComplement m

• Inputs:
  • m, a matrix, representing a homomorphism of free modules over a local ring
• Outputs:
  • a matrix, the complement of the image of the homomorphism represented by m

Description

i1 : R = ZZ/32003[x,y]

o1 = R

o1 : PolynomialRing

i2 : m = matrix{{x,y-1},{0,x}}

o2 = | x y-1 |
     | 0 x   |

             2       2
o2 : Matrix R  <--- R

i3 : setMaxIdeal(ideal(x,y))

o3 = ideal (x, y)

o3 : Ideal of R

i4 : localComplement m

o4 = | 0 |
     | 1 |

             2       1
o4 : Matrix R  <--- R

See also

• setMaxIdeal -- set the maximal ideal for local ring methods
• localsyz -- find syzygies
• localMingens -- finds a minimal set of generators
• localModulo -- find the pre-image (pullback) of image of a map over a local ring
• 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