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Dmodules :: generalB(List,RingElement)

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

Synopsis

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.

See also