Singular

LIB "fpaprops.lib";
ring r = 0,(x,y,z),dp;
def R = freeAlgebra(r, 5); // constructs a Letterplace ring
R;
==> // coefficients: QQ
==> // number of vars : 15
==> //        block   1 : ordering dp
==> //                  : names    x y z x y z x y z x y z x y z
==> //        block   2 : ordering C
==> // letterplace ring (block size 3, ncgen count 0)
setring R; // sets basering to Letterplace ring
ideal I = z;//an example of infinite GK dimension
teach_lpGkDim(I);
==> -1
I = x,y,z; // gkDim = 0
teach_lpGkDim(I);
==> 0
I = x*y, x*z, z*y, z*z;//gkDim = 2
teach_lpGkDim(I);
==> 2
ideal G = y*x - x*y, z*x - x*z, z*y - y*z; G = std(G);
G;
==> G[1]=z*y-y*z
==> G[2]=z*x-x*z
==> G[3]=y*x-x*y
teach_lpGkDim(G); // 3, as expected for K[x,y,z]
==> 3