# Singular

#### D.15.18.20 grlift

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

Usage:
grlift(M, N), graded objects M and N

Return:

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) ); ```