Singular

7.7.2.0. bfctAnn

Usage:

bfctAnn(f [,a,b,c]); f a poly, a, b, c optional ints

Return:

list of ideal and intvec

Purpose:

computes the roots of the Bernstein-Sato polynomial b(s) for the
hypersurface defined by f.

Assume:

The basering is commutative and of characteristic 0.

Background:

In this proc, Ann(f^s) is computed and then a system of linear
equations is solved by linear reductions.

Note:

In the output list, the ideal contains all the roots and the intvec
their multiplicities.
If a<>0, only f is appended to Ann(f^s), otherwise, and by default,
f and all its partial derivatives are appended.
If b<>0, std is used for GB computations, otherwise, and by
default, slimgb is used.
If c<>0, std is used for Groebner basis computations of ideals
<I+J> when I is already a Groebner basis of <I>.
Otherwise, and by default the engine determined by the switch b is used.
Note that in the case c<>0, the choice for b will be overwritten only
for the types of ideals mentioned above.
This means that if b<>0, specifying c has no effect.

Display:

If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

LIB "bfun.lib";
ring r = 0,(x,y),dp;
poly f = x^2+y^3+x*y^2;
bfctAnn(f);
==> [1]:
==>    _[1]=-5/6
==>    _[2]=-1
==>    _[3]=-7/6
==> [2]:
==>    1,1,1
def R = reiffen(4,5); setring R;
RC; // the Reiffen curve in 4,5
==> xy4+y5+x4
bfctAnn(RC,0,1);
==> [1]:
==>    _[1]=-9/20
==>    _[2]=-11/20
==>    _[3]=-13/20
==>    _[4]=-7/10
==>    _[5]=-17/20
==>    _[6]=-9/10
==>    _[7]=-19/20
==>    _[8]=-1
==>    _[9]=-21/20
==>    _[10]=-11/10
==>    _[11]=-23/20
==>    _[12]=-13/10
==>    _[13]=-27/20
==> [2]:
==>    1,1,1,1,1,1,1,1,1,1,1,1,1