Singular

7.7.7.0. lpHilbert

Usage:

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

Return:

intvec, containing the coefficients of the Hilbert series

Purpose:

Computing the Hilbert series

Assume:

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

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 I is 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
lpHilbert(G,5,2); // invokes procedure with degree bound 5 and 2 variables
==> 1,2,2,1
// note that the optional parameters are not necessary, due to the finiteness
// of the K-dimension of the factor algebra
lpDHilbert(G); // procedure with ring parameters
==> [1]:
==>    6
==> [2]:
==>    1,2,2,1
lpDHilbert(G,0); // procedure without degreebound
==> [1]:
==>    6
==> [2]:
==>    1,2,2,1