Singular

LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
module M = grtwists( intvec(-2, 0, 4, 4) ); grview(M);
==> Graded homomorphism: r(-2) + r + r(4)^2 <- 0, given by zero (4 x 0) matri\
   x.
module N = grgens(M);
grview( N ); print(N); // fine == M
==> Graded homomorphism: r(-2) + r + r(4)^2 <- r(-2) + r + r(4)^2, given by a\
    diagonal matrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ....
==>      --- --- --- --- +...
==>   2 :  0   -   -   - |..1
==>   0 :  -   0   -   - |..2
==>  -4 :  -   -   0   - |..3
==>  -4 :  -   -   -   0 |..4
==>      === === === ===     
==>        2   0  -4  -4     
==> 1,0,0,0,
==> 0,1,0,0,
==> 0,0,1,0,
==> 0,0,0,1 
module A = grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) );
A = grgroebner(A); grview(A);
==> Graded homomorphism: r^3 + r(-1) <- r(-1)^3 + r(-2) + r(-3), given by a m\
   atrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ....
==>      --- --- --- --- --- +...
==>   0 :  1   1   1   2   - |..1
==>   0 :  1   -   1   -   - |..2
==>   0 :  1   1   1   2   3 |..3
==>   1 :  0   0   0   1   2 |..4
==>      === === === === ===     
==>        1   1   1   2   3     
module B = grgens(A);
grview( B ); print(B); // Ups :( != A
==> Graded homomorphism: r(2) <- r^3 + r(-1), given by a matrix, with degrees\
   : 
==>      ..1 ..2 ..3 ..4 ....
==>      --- --- --- --- +...
==>  -2 :  2   2   2   3 |..1
==>      === === === ===     
==>        0   0   0   1     
==> xy-3y2+xz+3yz,-xy+2y2+2xz+2yz,x2-xy-4y2,y3-x2z-2xyz-y2z
grview( grgens( grzero() ) );
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.