Singular

7.5.4.0. bernsteinLift

Usage:

bernsteinLift(I, F [,eng]); I an ideal, F a poly, eng an optional int

Return:

list

Purpose:

compute the (multiple of) Bernstein-Sato polynomial with lift-like method,
based on the output of Sannfs-like procedure

Note:

the output list contains the roots with multiplicities of the candidate
for being Bernstein-Sato polynomial of f.
If eng <>0, std is used for Groebner basis computations,
otherwise and by default slimgb is used.
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),Dp;
poly F = x^3+y^3+z^3;
printlevel = 0;
def A = Sannfs(F);   setring A;
LD;
==> LD[1]=z^2*Dy-y^2*Dz
==> LD[2]=x*Dx+y*Dy+z*Dz-3*s
==> LD[3]=z^2*Dx-x^2*Dz
==> LD[4]=y^2*Dx-x^2*Dy
poly F = imap(r,F);
list L  = bernsteinLift(LD,F); L;
==> [1]:
==>    _[1]=-2
==>    _[2]=-4/3
==>    _[3]=-5/3
==>    _[4]=-1
==> [2]:
==>    1,1,1,2
poly bs = fl2poly(L,"s"); bs; // the candidate for Bernstein-Sato polynomial
==> s^5+7*s^4+173/9*s^3+233/9*s^2+154/9*s+40/9