Singular

LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
module A = 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, given by a matrix, with degr\
   ees: 
==>      ..1 ..2 ..3 ....
==>      --- --- --- +...
==>   0 :  1   -   1 |..1
==>   0 :  1   1   1 |..2
==>   0 :  -   1   1 |..3
==>   1 :  0   0   0 |..4
==>      === === ===     
==>        1   1   1     
module B = grgroebner(A);
grview(B);
==> 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     
"graded resolution of B: "; def C = grres(B, 0); grview(C);
==> graded resolution of B: 
==> Graded resolution: 
==> r^3 + r(-1) <-- d_1 --
==> r(-1) + r(-2) + r(-1)^2 + r(-3) <-- d_2 --
==> r(-3) + r(-2) <-- d_3 --
==> 0, given by maps: 
==> d_1 :
==> Graded homomorphism: r^3 + r(-1) <- r(-1) + r(-2) + r(-1)^2 + r(-3), give\
   n by a matrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ....
==>      --- --- --- --- --- +...
==>   0 :  1   2   1   1   - |..1
==>   0 :  -   -   1   1   - |..2
==>   0 :  1   2   1   1   3 |..3
==>   1 :  0   1   0   0   2 |..4
==>      === === === === ===     
==>        1   2   1   1   3     
==> d_2 :
==> Graded homomorphism: r(-1) + r(-2) + r(-1)^2 + r(-3) <- r(-3) + r(-2), gi\
   ven by a matrix, with degrees: 
==>      ..1 ..2 ....
==>      --- --- +...
==>   1 :  2   1 |..1
==>   2 :  1   0 |..2
==>   1 :  -   1 |..3
==>   1 :  -   1 |..4
==>   3 :  0   - |..5
==>      === ===     
==>        3   2     
==> d_3 :
==> Graded homomorphism: r(-3) + r(-2) <- 0, given by zero (2 x 0) matrix.
int i; int l = size(C);
"D^2 == 0: "; for (i = 1; i < l; i++ ) { i; grview( grprod(C[i], C[i+1]) ); }
==> D^2 == 0: 
==> 1
==> Graded homomorphism: r^3 + r(-1) <- r(-3) + r(-2), given by zero (4 x 2) \
   matrix.
==> 2
==> Graded homomorphism: r(-1) + r(-2) + r(-1)^2 + r(-3) <- 0, given by zero \
   (5 x 0) matrix.