
7.5.7 dmodvar_lib
 Library:
 dmodvar.lib
 Purpose:
 Algebraic Dmodules for varieties
 Authors:
 Daniel Andres, daniel.andres@math.rwthaachen.de
Viktor Levandovskyy, levandov@math.rwthaachen.de
Jorge MartinMorales, 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 nth 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 rtuple 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: BernsteinSato polynomials of arbitrary varieties (2006).
(ALM09) Andres, Levandovskyy, MartinMorales: Principal Intersection and BernsteinSato
Polynomial of an Affine Variety (2009).
Procedures:
7.5.7.0. bfctVarIn   computes the roots of the BernsteinSato polynomial b(s) of the variety V(F) using initial ideal approach 
7.5.7.0. bfctVarAnn   computes the roots of the BernsteinSato 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] 
See also:
bfun_lib;
dmod_lib;
dmodapp_lib;
gmssing_lib.
