##### 7.5.6.0. BSidealFromAnn

Procedure from library `dmodideal.lib` (see dmodideal_lib).

Usage:
  BSidealFromAnn(F, @R [,eng,met]); F an ideal, @R a ring, eng, met optional ints

Return:
  ring

Purpose:
  compute several kinds of Bernstein-Sato ideals, associated to f = F[1]*..*F[P], with the multivariate algorithm by Briancon and Maisonobe from ann(F^s) as input.

Assume:
  basering is a commutative polynomial ring in characteristic 0 @R is a ring as returned from annihilatorMultiFs.

Note:
  activate the output ring with the `setring` command. In this ring, the ideal BS is a Bernstein-Sato ideal of a polynomial f = F[1]*..*F[P]. If eng <>0, `std` is used for Groebner basis computations, otherwise, and by default `slimgb` is used. If met is of type int:
  if met <0, the B-Sigma ideal (cf. (CU)) is computed.
  If 0 < met < P, then the ideal B_met (cf. (CU)) is computed. If met is an intvec or a list of intvecs, Budurs generalized Bernstein-Sato ideal associated to met is computed.
  Otherwise, and by default, the ideal B (cf. (CU)) is computed. If met is of type intvec:
  Budurs generalized Bernstein-Sato ideal B^met_F is computed. If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed.

Example:

    LIB "dmodideal.lib";
    ring R = 0,(x,y),dp;
    ideal F = x+y,x-y,x;
    def @R = annihilatorMultiFs(F, 0, 0, 4);
    // first we compute the ideal B
    def @R2 = BSidealFromAnn(F, @R, 0, 0);
    setring @R2;
    BS;
    ==> BS[1]=s(1)^4*s(2)*s(3)+s(1)^4*s(2)+s(1)^4*s(3)+s(1)^4+3*s(1)^3*s(2)^2*s(3\
       )+3*s(1)^3*s(2)^2+3*s(1)^3*s(2)*s(3)^2+16*s(1)^3*s(2)*s(3)+13*s(1)^3*s(2)\
       +3*s(1)^3*s(3)^2+13*s(1)^3*s(3)+10*s(1)^3+3*s(1)^2*s(2)^3*s(3)+3*s(1)^2*s\
       (2)^3+6*s(1)^2*s(2)^2*s(3)^2+30*s(1)^2*s(2)^2*s(3)+24*s(1)^2*s(2)^2+3*s(1\
       )^2*s(2)*s(3)^3+30*s(1)^2*s(2)*s(3)^2+83*s(1)^2*s(2)*s(3)+56*s(1)^2*s(2)+\
       3*s(1)^2*s(3)^3+24*s(1)^2*s(3)^2+56*s(1)^2*s(3)+35*s(1)^2+s(1)*s(2)^4*s(3\
       )+s(1)*s(2)^4+3*s(1)*s(2)^3*s(3)^2+16*s(1)*s(2)^3*s(3)+13*s(1)*s(2)^3+3*s\
       (1)*s(2)^2*s(3)^3+30*s(1)*s(2)^2*s(3)^2+83*s(1)*s(2)^2*s(3)+56*s(1)*s(2)^\
       2+s(1)*s(2)*s(3)^4+16*s(1)*s(2)*s(3)^3+83*s(1)*s(2)*s(3)^2+162*s(1)*s(2)*\
       s(3)+94*s(1)*s(2)+s(1)*s(3)^4+13*s(1)*s(3)^3+56*s(1)*s(3)^2+94*s(1)*s(3)+\
       50*s(1)+s(2)^4*s(3)+s(2)^4+3*s(2)^3*s(3)^2+13*s(2)^3*s(3)+10*s(2)^3+3*s(2\
       )^2*s(3)^3+24*s(2)^2*s(3)^2+56*s(2)^2*s(3)+35*s(2)^2+s(2)*s(3)^4+13*s(2)*\
       s(3)^3+56*s(2)*s(3)^2+94*s(2)*s(3)+50*s(2)+s(3)^4+10*s(3)^3+35*s(3)^2+50*\
       s(3)+24
    setring R;
    // secondly we compute the ideal B_1
    @R2 = BSidealFromAnn(F, @R, 0, 1);
    setring @R2;
    BS;
    ==> BS[1]=s(1)^2+s(1)*s(2)+s(1)*s(3)+3*s(1)+s(2)+s(3)+2

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