Singular Manual: sickle

| ##### 7.7.7.0. sickle Procedure from library `fpadim.lib` (see fpadim_lib). Usage: sickle(G[,m, d, h, degbound]); G an ideal; m,d,h,degbound optional integers Return: list Purpose: Allowing the user to access all procs with one command 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: The returned object will always be a list, but the entries of the returned list may be very different case m=1,d=1,h=1: see lpDHilbertSickle case m=1,d=1,h=0: see lpSickleDim case m=1,d=0,h=1: see lpSickleHil case m=1,d=0,h=0: see lpSickle (this is the default case) case m=0,d=1,h=1: see lpDHilbert case m=0,d=1,h=0: see lpKDim case m=0,d=0,h=1: see lpHilbert case m=0,d=0,h=0: returns an error - If degbound is set, there will be a degree bound added. 0 means no degree bound. Default: attrib(basering,uptodeg). - 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);
    // G contains a Groebner basis
    sickle(G,1,1,1); // computes mistletoes, K-dimension and the Hilbert series
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    1,2,2,1
    ==> [3]:
    ==>    _[1]=x(1)*y(2)
    ==>    _[2]=y(1)*x(2)*y(3)
    sickle(G,1,0,0); // computes mistletoes only
    ==> _[1]=x(1)*y(2)
    ==> _[2]=y(1)*x(2)*y(3)
    sickle(G,0,1,0); // computes K-dimension only
    ==> 6
    sickle(G,0,0,1); // computes Hilbert series only
    ==> 1,2,2,1

User manual for Singular version 4-1-0, 2016, generated by texi2html.