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D.15.6.20 grlift
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grlift(M, N), graded objects M and N
- Return:
- transformation matrix (graded object???)
- Purpose:
- compute graded matrix which the generators of submodule Im(N) in terms of Im(M).
Example:
| LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
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
def G=grlift(D,P);
grview(G);
==> Graded homomorphism: r(-1) + r(-2) <- r(-2), given by a matrix, with degr\
ees:
==> ..1 ....
==> --- +...
==> 1 : 1 |..1
==> 2 : - |..2
==> ===
==> 2
ASSUME(0, grisequal( grprod(D, G), P) );
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