Singular Manual: lpDHilbert

| ##### 7.7.7.0. lpDHilbert Procedure from library `fpadim.lib` (see fpadim_lib). Usage: lpDHilbert(G[,degbound,n]); G an ideal, degbound, n optional integers Return: list Purpose: Computing K-dimension and Hilbert series, starting with a lp-ideal 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 corresponding to the dimension, L[2] is an intvec which contains the coefficients of the Hilbert series - 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[2] 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
    lpDHilbert(G,5,2); // invokes procedure with degree bound 5 and 2 variables
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    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

User manual for Singular version 4-0-3p3, 2016, generated by texi2html.