Singular

D.15.14.28 grlifting2

Procedure from library `gradedModules.lib` (see gradedModules_lib).

Usage:
grlifting2(A,B), graded objects A and B (matrices defining maps)

Return:
map of chain complexes (as a list)

Purpose:
construct a map of chain complexes between free resolution of M=coker(A) and N=coker(B).

Example:
 ```LIB "gradedModules.lib"; ring r; module P=grobj(module([xy,0,xz]),intvec(0,1,0)); grview(P); ==> Graded homomorphism: r + r(-1) + r <- r(-2), given by a matrix, with degr\ ees: ==> ..1 .... ==> --- +... ==> 0 : 2 |..1 ==> 1 : - |..2 ==> 0 : 2 |..3 ==> === ==> 2 module D=grobj(module([y,0,z],[x2+y2,z,0]),intvec(0,1,0)); grview(D); ==> Graded homomorphism: r + r(-1) + r <- r(-1) + r(-2), given by a matrix, w\ ith degrees: ==> ..1 ..2 .... ==> --- --- +... ==> 0 : 1 2 |..1 ==> 1 : - 1 |..2 ==> 0 : 1 - |..3 ==> === === ==> 1 2 module PP = grpres(P); grview(PP); ==> Graded homomorphism: r(-2) <- 0, given by zero (1 x 0) matrix. module DD = grpres(D); grview(DD); ==> Graded homomorphism: r(-1) + r(-2) <- 0, given by zero (2 x 0) matrix. def T=grlifting2(DD,PP); T; ==> T[1]=0 ==> T[2]=-5361*gen(1) // def Z=grlifting2(P,D); Z; // WRONG!!! ```