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# 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

## See also

- bFunction -- b-function
- globalBFunction -- global b-function (else known as the Bernstein-Sato polynomial)
- factorBFunction -- factorization of a b-function

## 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/bFunctions.m2:336:0.