##### 7.7.7.0. lpDHilbertSickle

Procedure from library `fpadim.lib` (see fpadim_lib).

Usage:
  lpDHilbertSickle(G[,degbound,n]); G an ideal, degbound, n optional
  integers

Return:
  list

Purpose:
  Computing K-dimension, Hilbert series and mistletoes at once

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 integer, the K-dimension,
  L[2] is an intvec, the Hilbert series and L[3] 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 can be set to a different number of variables.
  Default: n = 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
    lpDHilbertSickle(G,5,2); //invokes procedure with degree bound 5 and 2 variables
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    1,2,2,1
    ==> [3]:
    ==>    _[1]=x(1)*y(2)
    ==>    _[2]=y(1)*x(2)*y(3)
    // note that the optional parameters are not necessary, due to the finiteness
    // of the K-dimension of the factor algebra
    lpDHilbertSickle(G); // procedure with ring parameters
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    1,2,2,1
    ==> [3]:
    ==>    _[1]=x(1)*y(2)
    ==>    _[2]=y(1)*x(2)*y(3)
    lpDHilbertSickle(G,0); // procedure without degreebound
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    1,2,2,1
    ==> [3]:
    ==>    _[1]=x(1)*y(2)
    ==>    _[2]=y(1)*x(2)*y(3)

User manual for Singular version 4-0-3, 2016, generated by texi2html.