Singular

7.7.4.0. bernsteinBM

Usage:

bernsteinBM(f [,eng]); f a poly, eng an optional int

Return:

list (of roots of the Bernstein polynomial b and their multiplicies)

Purpose:

compute the global Bernstein-Sato polynomial for a hypersurface,
defined by f, according to the algorithm by Briancon and Maisonobe

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,z,w),Dp;
poly F = x^3+y^3+z^2*w;
printlevel = 0;
bernsteinBM(F);
==> [1]:
==>    _[1]=-2
==>    _[2]=-3/2
==>    _[3]=-7/3
==>    _[4]=-7/6
==>    _[5]=-11/6
==>    _[6]=-1
==>    _[7]=-5/3
==> [2]:
==>    1,1,1,1,1,1,1