Singular

7.7.4.0. checkFactor

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.

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