# Singular

##### 7.7.7.0. lpSickleHil
Procedure from library `fpadim.lib` (see fpadim_lib).

Usage:
lpSickleHil(G);

Return:
list

Purpose:
Computing the Hilbert series and the mistletoes

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 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

Example:
 ```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) ```