Singular

LIB "gkdim.lib";
ring R = 0,(x,y,z),Dp;
matrix C[3][3]=0,1,1,0,0,-1,0,0,0;
matrix D[3][3]=0,0,0,0,0,x;
def r = nc_algebra(C,D); setring r;
r;
==> // coefficients: QQ
==> // number of vars : 3
==> //        block   1 : ordering Dp
==> //                  : names    x y z
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    zy=-yz+x
ideal I=x;
GKdim(I);
==> 2
ideal J=x2,y;
GKdim(J);
==> 1
module M=[x2,y,1],[x,y2,0];
GKdim(M);
==> 3
ideal A = x,y,z;
GKdim(A);
==> 0
ideal B = 1;
GKdim(B);
==> -1
GKdim(ideal(0)) == nvars(basering);  // should be true, i.e., evaluated to 1
==> 1