Singular

7.7.2.0. bfctSyz

Usage:

bfctSyz(f [,r,s,t,u,v]); f poly, r,s,t,u optional ints, v opt. intvec

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, the initial Malgrange ideal is computed according to
the algorithm by Masayuki Noro and then a system of linear equations is
solved by computing syzygies.

Note:

In the output list, the ideal contains all the roots and the intvec
their multiplicities.
If r<>0, std is used for GB computations in characteristic 0,
otherwise, and by default, slimgb is used.
If s<>0, a matrix ordering is used for GB computations, otherwise,
and by default, a block ordering is used.
If t<>0, the computation of the intersection is solely performed over
charasteristic 0, otherwise and by default, a modular method is used.
If u<>0 and by default, std is used for GB computations in
characteristic >0, otherwise, slimgb is used.
If v is a positive weight vector, v is used for homogenization
computations, otherwise and by default, no weights are used.

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;
bfctSyz(f);
==> [1]:
==>    _[1]=-5/6
==>    _[2]=-1
==>    _[3]=-7/6
==> [2]:
==>    1,1,1
intvec v = 3,2;
bfctSyz(f,0,1,1,0,v);
==> [1]:
==>    _[1]=-5/6
==>    _[2]=-1
==>    _[3]=-7/6
==> [2]:
==>    1,1,1