
7.7.2.0. 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 BernsteinSato 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);
==> [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

