modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)

Synopsis

• Function: modulo

• Usage:

  modulo(f,g)

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

Description

The maps f and g must have the same target, and their sources and targets must be free. If f is null, then it is taken to be the identity. If g is null, it is taken to be zero.

This function is mainly for internal use.

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

o1 = R

o1 : PolynomialRing

i2 : f = matrix {{x,y}}

o2 = | x y |

             1       2
o2 : Matrix R  <--- R

i3 : g = matrix {{y,z}}

o3 = | y z |

             1       2
o3 : Matrix R  <--- R

i4 : modulo(f,g)

o4 = {1} | 0 z y |
     {1} | 1 0 0 |

             2       3
o4 : Matrix R  <--- R

i5 : kernel( inducedMap(coker g, target g) * f )

o5 = image {1} | 0 z y |
           {1} | 1 0 0 |

                             2
o5 : R-module, submodule of R