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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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