Singular

7.7.7.0. lpSickleHil

Usage:

lpSickleHil(G);

Return:

list

Purpose:

Computing the Hilbert series and the mistletoes

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 intvec, corresponding to the
Hilbert series, 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 I = L[1] is the intvec returned, then I[k] is the (k-1)-th
coefficient of the Hilbert series.
- 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
lpSickleHil(G); // invokes the procedure with ring parameters
==> [1]:
==>    1,2,2,1
==> [2]:
==>    _[1]=x(1)*y(2)
==>    _[2]=y(1)*x(2)*y(3)
// the factor algebra is finite, so the degree bound given by the Letterplace
// ring is not necessary
lpSickleHil(G,0); // procedure without any degree bound
==> [1]:
==>    1,2,2,1
==> [2]:
==>    _[1]=x(1)*y(2)
==>    _[2]=y(1)*x(2)*y(3)