generalB(List,RingElement) -- global generalized Bernstein-Sato polynomial

Synopsis

Function: generalB
Usage:

b = generalB(F,g), b = generalB F
Inputs:
- F, a list of polynomials
- g, a polynomial
Optional inputs:
- Exponent => ..., default value null, specify exponent m for m-generalized Bernstein-Sato polynomial
- Strategy => ..., default value InitialIdeal, specify strategy for computing generalized Bernstein-Sato polynomial
Outputs:
- b, a ring element, the general Bernstein-Sato polynomial b(s) in Q[s]

Description

Bernstein-Sato polynomial for an arbitrary affine variety was introduced in Budur, Mustata, and Saito ``Bernstein--Sato polynomials of arbitrary varieties''. If the option Exponent is specified, then the m-generalized Bernstein-Sato polynomial is computed. See Berkesch and Leykin ``Algorithms for Bernstein-Sato polynomials and multiplier ideals'' for definitions.

i1 : W = makeWA(QQ[x_1..x_3]);

i2 : factorBFunction generalB ({x_2^2-x_1*x_3, x_1^3-x_3^2}, x_2)

                 5      9      11      11      13      29      31      35      37
o2 = (s + 2)(s + -)(s + -)(s + --)(s + --)(s + --)(s + --)(s + --)(s + --)(s + --)
                 2      4       4       6       6      12      12      12      12

o2 : Expression of class Product

Caveat

The input could be either in a polynomial ring or the Weyl algebra. In the latter case the algebra should not have any central variables and should not be a homogeneous Weyl algebra.

Ways to use this method: