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

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