# Singular

##### 7.7.8.0. 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 it is positive infinite

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

Example:
 ```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 ```