localBFunction(RingElement,Ideal) -- local b-function (a.k.a. the local Bernstein-Sato polynomial)

Synopsis

• Function: localBFunction

• Usage:

  b = localBFunction(f,P)

• Inputs:
  • f, a polynomial
  • P, a (prime) ideal
• Outputs:
  • b, a ring element, the local b-function b_P(s) in Q[s]

Description

Computes the local b-function of f at P, if P is a prime ideal.

i1 : R = QQ[x,y]; f = x^2*(x+y+1); P = ideal(x,y);

o3 : Ideal of R

i4 : b = localBFunction(f,P)

      2   3    1
o4 = s  + -s + -
          2    2

o4 : QQ[s]

i5 : factorBFunction b

                 1
o5 = (s + 1)(s + -)
                 2

o5 : Expression of class Product

Caveat

See also

• bFunction -- b-function
• factorBFunction -- factorization of a b-function
• globalBFunction -- global b-function (else known as the Bernstein-Sato polynomial)
• generalB -- global generalized Bernstein-Sato polynomial
• globalB -- compute global b-function and b-operator for a D-module and a polynomial