Singular Manual: checkFactor

| ##### 7.5.4.0. checkFactor Procedure from library `dmod.lib` (see dmod_lib). Usage: checkFactor(I,f,qs [,eng]); I an ideal, f a poly, qs a poly, eng an optional int Assume: checkFactor is called from the basering, created by Sannfs-like proc, that is, from the Weyl algebra in x1,..,xN,d1,..,dN tensored with K[s]. The ideal I is the annihilator of f^s in D[s], that is the ideal, computed by Sannfs-like procedure (usually called LD there). Moreover, f is a polynomial in K[x1,..,xN] and qs is a polynomial in K[s]. Return: int, 1 if qs is a factor of the global Bernstein polynomial of f and 0 otherwise Purpose: check whether a univariate polynomial qs is a factor of the Bernstein-Sato polynomial of f without explicit knowledge of the latter. Note: If eng <>0, `std` is used for Groebner basis computations, otherwise (and by default) `slimgb` is used. Display: If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed. Example:
    LIB "dmod.lib";
    ring r = 0,(x,y),Dp;
    poly F = x^4+y^5+x*y^4;
    printlevel = 0;
    def A = Sannfs(F);
    setring A;
    poly F = imap(r,F);
    checkFactor(LD,F,20*s+31);     // -31/20 is not a root of bs
    ==> 0
    checkFactor(LD,F,20*s+11);     // -11/20 is a root of bs
    ==> 1
    checkFactor(LD,F,(20*s+11)^2); // the multiplicity of -11/20 is 1
    ==> 0

User manual for Singular version 4.3.2, 2023, generated by texi2html.