Singular Manual: bfctAnn

| ##### 7.5.2.0. bfctAnn Procedure from library `bfun.lib` (see bfun_lib). 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. Example:
    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

User manual for Singular version 4-2-0p1, 2020, generated by texi2html.