
7.5.6 dmodideal_lib
 Library:
 dmodideal.lib
 Purpose:
 Algorithms for BernsteinSato ideals of morphisms
 Authors:
 Robert Loew, robert.loew at rwthaachen.de
Viktor Levandovskyy, levandov at math.rwthaachen.de
Jorge Martin Morales, jorge at unizar.es
 Overview:
 Let K be a field of characteristic 0. Given a polynomial ring
R = K[x_1,...,x_n] and a map, given by polynomials F_1,...,F_r from R,
one is interested in the R[1/(F_1*...*F_r)]module of rank one, generated by
the symbol F^s=F_1^(s_1)*...*F_r^(s_r) for symbolic discrete variables s_1,...,s_r.
This module R[1/(F_1*...*F_r)]*F^s has a structure of a D(R)[s_1,...,s_r]module, where D(R)
is an nth Weyl algebra K<x_1,...,x_n,d_1,...,d_n  d_j x_j = x_j d_j +1> and
D(R)[s] := D(R) tensored with K[s]:=K[s_1,...,s_r] over K.
We often write just D for D(R) and D[s] for D(R)[s].
One is interested in the computation of the following data:
 Ann_{D[s]} F^s, the annihilator of F^s in D[s]; see annihilatorMultiFs
 Ann^{1}_{D[s]} F^s, the logarithmic annihilator of F^s in D[s]; see annfsLogIdeal
 several kinds of global BernsteinSato ideals in K[s],
cf. (CU) and (Bud12); see BernsteinSatoIdeal and BSidealFromAnn
 Ann_{D} F^alpha for alpha from K^r, the annihilator of F^alpha in D; see annfalphaI
 sub and overideals, bounding the BernsteinSato ideal; see BFBoundsBudur
 References:
 (BM) the Ann F^s algorithm by Briancon and Maisonobe (Remarques sur
l'ideal de Bernstein associe a des polynomes, preprint, 2002)
(LM08) V. Levandovskyy and J. MartinMorales, ISSAC 2008
(CU) Castro and Ucha, On the computation of BernsteinSato ideals, JSC 2005
(SST) Saito, Sturmfels, Takayama 'Groebner Deformations of Hypergeometric
Differential Equations', Springer, 2000
(Bud12) N. Budur, BernsteinSato ideals and local systems, Annales de
l'Institut Fourier, Volume 65 (2015) no. 2
(OT99) T. Oaku and N. Takayama, An algorithm for de Rham cohomology groups of
the complement of an affine variety via Dmodule computation,
Journal of Pure and Applied Algebra, 1999
Procedures:
See also:
bfun_lib;
dmod_lib;
dmodapp_lib;
dmodloc_lib;
gmssing_lib.
