|  |  7.5.7 dmodvar_lib 
Library:
dmodvar.lib
Purpose:
     Algebraic D-modules for varieties
Authors:
Daniel Andres, daniel.andres@math.rwth-aachen.de
Viktor Levandovskyy, levandov@math.rwth-aachen.de
 Jorge Martin-Morales, jorge@unizar.es
 
Support: DFG Graduiertenkolleg 1632 'Experimentelle und konstruktive Algebra'
 
Overview:
Let K be a field of characteristic 0. Given a polynomial ring R = K[x_1,...,x_n]
and polynomials f_1,...,f_r in R, define F = f_1*...*f_r and F^s = f_1^s_1*...*f_r^s_r
for symbolic discrete (that is shiftable) variables s_1,..., s_r.
The module R[1/F]*F^s has the structure of a D<S>-module, where D<S> = D(R)
tensored with S over K, where
- D(R) is the n-th Weyl algebra K<x_1,...,x_n,d_1,...,d_n | d_j x_j = x_j d_j + 1>
 - S is the universal enveloping algebra of gl_r, generated by s_i = s_{ii}.
 One is interested in the following data:
 - the left ideal Ann F^s in D<S>, usually denoted by LD in the output
 - global Bernstein polynomial in one variable s = s_1+...+s_r, denoted by bs,
 - its minimal integer root s0, the list of all roots of bs, which are known to be
negative rational numbers, with their multiplicities, which is denoted by BS
 - an r-tuple of operators in D<S>, denoted by PS, such that the functional equality
sum(k=1 to k=r) P_k*f_k*F^s = bs*F^s holds in R[1/F]*F^s.
 
References:
(BMS06) Budur, Mustata, Saito: Bernstein-Sato polynomials of arbitrary varieties (2006).
(ALM09) Andres, Levandovskyy, Martin-Morales: Principal Intersection and Bernstein-Sato
Polynomial of an Affine Variety (2009).
 
 
Procedures:
 See also:
 bfun_lib;
 dmod_lib;
 dmodapp_lib;
 gmssing_lib. 
| 7.5.7.0. bfctVarIn |  | computes the roots of the Bernstein-Sato polynomial b(s) of the variety V(F) using initial ideal approach |  | 7.5.7.0. bfctVarAnn |  | computes the roots of the Bernstein-Sato polynomial b(s) of the variety V(F) using Sannfs approach |  | 7.5.7.0. SannfsVar |  | computes the annihilator of F^s in the ring D<S> |  | 7.5.7.0. makeMalgrange |  | creates the Malgrange ideal, associated with F = F[1],..,F[P] | 
 
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