Singular

7.10.1.5 lpSickleDim

Usage:

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

Return:

list

Purpose:

Compute the K-dimension and the mistletoes of K<X>/<G>

Assume:

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

Note:

- If L is the list returned, then L[1] is an integer, the K-dimension,
L[2] is an ideal, the mistletoes.
- 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 = freeAlgebra(r, 5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
ideal G = x*x, y*y,x*y*x; // G is a monomial Groebner basis
lpSickleDim(G); // invokes the procedure with ring parameters
==> [1]:
==>    6
==> [2]:
==>    _[1]=x*y
==>    _[2]=y*x*y
// the factor algebra is finite, so the degree bound, given
// by the Letterplace ring is not necessary
lpSickleDim(G,0); // procedure without any degree bound
==> [1]:
==>    6
==> [2]:
==>    _[1]=x*y
==>    _[2]=y*x*y