Singular

7.7.8.0. lpGlDimBound

Usage:

lpGlDimBound(I); I an ideal

Return:

int, an upper bound for the global dimension, -1 means infinity

Purpose:

computing an upper bound for the global dimension

Assume:

- basering is a Letterplace ring, G is a reduced Groebner Basis

Note:

if I = LM(I), then the global dimension is equal the Gelfand Kirillov dimension if it is finite
Global dimension should be 0 for A/G = K and 1 for A/G = K<x1...xn>

LIB "fpaprops.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
ideal G = x(1)*x(2), y(1)*y(2),x(1)*y(2)*x(3); // ideal G contains a
//Groebner basis
lpGlDimBound(G); // invokes procedure with Groebner basis G
==> 0