Singular

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) );