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

## Synopsis

• Function: globalB
• Usage:
H = globalB(I,f)
• Inputs:
• I, an ideal, a holonomic ideal
• f, , a polynomial in a Weyl algebra (should not contain differential variables)
• Outputs:
• H, , 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 variables 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