Singular

LIB "fpaprops.lib";
ring r = 0,(x,y,z),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
R;
==> // coefficients: QQ
==> // number of vars : 15
==> //        block   1 : ordering a
==> //                  : names    x(1) y(1) z(1) x(2) y(2) z(2) x(3) y(3) z(\
   3) x(4) y(4) z(4) x(5) y(5) z(5)
==> //                  : weights     1    1    1    1    1    1    1    1   \
    1    1    1    1    1    1    1
==> //        block   2 : ordering dp
==> //                  : names    x(1) y(1) z(1)
==> //        block   3 : ordering dp
==> //                  : names    x(2) y(2) z(2)
==> //        block   4 : ordering dp
==> //                  : names    x(3) y(3) z(3)
==> //        block   5 : ordering dp
==> //                  : names    x(4) y(4) z(4)
==> //        block   6 : ordering dp
==> //                  : names    x(5) y(5) z(5)
==> //        block   7 : ordering C
setring R; // sets basering to Letterplace ring
ideal I = z(1);//an example of infinite GK dimension
lpGkDim(I);
==> -1
I = x(1),y(1),z(1); // gkDim = 0
lpGkDim(I);
==> 0
I = x(1)*y(2), x(1)*z(2), z(1)*y(2), z(1)*z(2);//gkDim = 2
lpGkDim(I);
==> 2