Singular

7.7.7.0. lpKDim

Usage:

lpKDim(G[,degbound, n]); G an ideal, degbound, n optional integers

Return:

int, the K-dimension of the factor algebra

Purpose:

Computing the K-dimension of a factor algebra, given via an ideal

Assume:

- basering is a Letterplace ring
- if you specify a different degree bound degbound,
degbound <= attrib(basering,uptodeg) holds.

Note:

- If degbound is set, there will be a degree bound added. 0 means no
degree bound. Default: attrib(basering, uptodeg).
- n is the number of variables, which can be set to a different number.
Default: attrib(basering, lV).
- If the K-dimension is known to be infinite, a degree bound is needed

LIB "fpadim.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
lpKDim(G); //procedure invoked with ring parameters
==> 6
// the factor algebra is finite, so the degree bound given by the Letterplace
// ring is not necessary
lpKDim(G,0); // procedure without any degree bound
==> 6