globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and a polynomial

Function: globalB
Usage:

H = globalB(I,f)
Inputs:
- I, an ideal, a holonomic ideal
- f, a ring element, a polynomial in a Weyl algebra (should not contain differential variables)
Outputs:
- H, a hash table, containing the keys Bpolynomial and Boperator

Description

The algorithm used here is a modification of the original algorithm of Oaku for computing Bernstein-Sato polynomials

i1 : R = QQ[x, dx, WeylAlgebra => {x=>dx}]

o1 = R

o1 : PolynomialRing, 1 differential variable(s)

i2 : f = x^7

      7
o2 = x

o2 : R

i3 : b = globalB(ideal dx, f)

                              7
o3 = HashTable{Boperator => dx                                                                                   }
                                     7           6           5           4           3          2
               Bpolynomial => 823543s  + 3294172s  + 5411854s  + 4705960s  + 2321767s  + 643468s  + 91476s + 5040

o3 : HashTable

i4 : factorBFunction b.Bpolynomial 

                 1      2      3      4      5      6
o4 = (s + 1)(s + -)(s + -)(s + -)(s + -)(s + -)(s + -)
                 7      7      7      7      7      7

o4 : Expression of class Product

Ways to use this method:

globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and a polynomial

The source of this document is in BernsteinSato/DOC/bFunctions.m2:336:0.

globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and a polynomial

Description

See also

Ways to use this method: