Singular Manual: bfct

| ##### 7.5.2.0. bfct Procedure from library `bfun.lib` (see bfun_lib). Usage: bfct(f [,s,t,v]); f a poly, s,t optional ints, v an optional 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 linear reductions. Note: In the output list, the ideal contains all the roots and the intvec their multiplicities. If s<>0, `std` is used for GB computations, otherwise, and by default, `slimgb` is used. If t<>0, a matrix ordering is used for Groebner basis computations, otherwise, and by default, a block ordering 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;
    bfct(f);
    ==> [1]:
    ==>    _[1]=-5/6
    ==>    _[2]=-1
    ==>    _[3]=-7/6
    ==> [2]:
    ==>    1,1,1
    intvec v = 3,2;
    bfct(f,1,0,v);
    ==> [1]:
    ==>    _[1]=-5/6
    ==>    _[2]=-1
    ==>    _[3]=-7/6
    ==> [2]:
    ==>    1,1,1

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