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7.10.3.4 lpGkDim

Procedure from library fpaprops.lib (see fpaprops_lib).

Usage:
lpGkDim(G); G an ideal in a letterplace ring

Return:
int

Purpose:
Determines the Gelfand Kirillov dimension of A/<G>
-1 means positive infinite

Assume:
- basering is a Letterplace ring
- G is a Groebner basis

Note:
Alias for dim(G)

Example:
 
LIB "fpaprops.lib";
ring r = 0,(x,y,z),dp;
ring R = freeAlgebra(r, 5);
ideal I = z; // infinite GK dimension (-1)
lpGkDim(I);
==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
==> -1
I = x,y,z; I = std(I); // GK dimension 0
lpGkDim(I);
==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
==> 0
I = x*y, x*z, z*y, z*z; I = std(I); // GK dimension 2
lpGkDim(I);
==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
==> 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
lpGkDim(G); // GK dimension 3
==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
==> 3