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 = grsyz( grtranspose( M ) ); grview(N);
==> 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     
module L = grtranspose(N); grview( L );
==> 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     
module K = grsyz( L ); grview(K);
==> Graded homomorphism: r(-2) + r + r(4)^2 <- 0, given by zero (4 x 0) matri\
   x.
// Corner cases: 0 <- 0!
module Z = grzero(); grview(Z);
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
grview( grtranspose( Z ) );
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
// Corner cases: * <- 0
matrix M1[3][0];
module Z1 = grobj( M1, intvec(-1, 0, 1) ); grview(Z1);
==> Graded homomorphism: r(1) + r + r(-1) <- 0, given by zero (3 x 0) matrix.
grview( grtranspose( Z1 ) );
==> Graded homomorphism: 0 <- r(-1) + r + r(1), given by zero (0 x 3) matrix.
// Corner cases: 0 <- *
matrix M2[0][3];
module Z2 = grobj( M2, 0:0, intvec(-1, 0, 1) ); grview(Z2);
==> Graded homomorphism: 0 <- r(1) + r + r(-1), given by zero (0 x 3) matrix.
grview( grtranspose( Z2 ) );
==> Graded homomorphism: r(-1) + r + r(1) <- 0, given by zero (3 x 0) matrix.