Singular

LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
module A = grgroebner( grobj( module([x+y, x, 0, 3], [0, x+y, y, 2], [y, y, z, 1]), intvec(0,0,0,1) ) );
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     
grview(grsyz(A));
==> Graded homomorphism: r(-1)^3 + r(-2) + r(-3) <- r(-2) + r(-3), given by a\
    matrix, with degrees: 
==>      ..1 ..2 ....
==>      --- --- +...
==>   1 :  1   - |..1
==>   1 :  1   2 |..2
==>   1 :  1   - |..3
==>   2 :  0   1 |..4
==>   3 :  -   0 |..5
==>      === ===     
==>        2   3     
module X = grgroebner( grobj( module([x]), intvec(2) ) );
grview(X);
==> Graded homomorphism: r(-2) <- r(-3), given by a diagonal matrix, with deg\
   rees: 
==>     .1 ...
==>     -- +..
==>  2 : 1 |.1
==>     ==    
==>      3    
// syzygy module should be zero!
grview(grsyz(X));
==> Graded homomorphism: r(-3) <- 0, given by zero (1 x 0) matrix.