Singular

7.10.3.4 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 = freeAlgebra(r, 5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
ideal G = x*x, y*y,x*y*x; // it is a monomial Groebner basis
lpGlDimBound(G);
==> // ** G is no standard basis
==> 0
ideal H = y*x - x*y; H = std(H); // H is a Groebner basis
lpGlDimBound(H); // gl dim of K[x,y] is 2, as expected
==> 2