# Singular          ##### 7.5.2.0. bfctSyz
Procedure from library `bfun.lib` (see bfun_lib).

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.

Example:
 ```LIB "bfun.lib"; ring r = 0,(x,y),dp; poly f = x^2+y^3+x*y^2; bfctSyz(f); ==> : ==> _=-5/6 ==> _=-1 ==> _=-7/6 ==> : ==> 1,1,1 intvec v = 3,2; bfctSyz(f,0,1,1,0,v); ==> : ==> _=-5/6 ==> _=-1 ==> _=-7/6 ==> : ==> 1,1,1 ```

### Misc 