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D.15.6.28 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!!!
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