# paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients

## Synopsis

• Function: paramBpoly
• Usage:
paramBpoly(f,filename)
• Inputs:
• f, , a polynomial in Weyl algebra A_n(Q)
• filename, , the base name for the output files
• Optional inputs:
• GroundField => ..., default value 32749, characteristic for modular computation
• Outputs:
• a list, all possible Bernstein-Sato polynomials

## Description

 i1 : A = (QQ [a,b,c]) [x, y, Dx, Dy, WeylAlgebra => {x=>Dx, y=>Dy}] o1 = A o1 : PolynomialRing, 2 differential variables i2 : paramBpoly(a*x^2 + b*x*y + c*y^2, "quadratic") 2 1 o2 = {(S + 1) , (S + -)(S + 1)} 2 o2 : List

## Caveat

A finite field should be used in place of Q in order to speed up computations. This routine works only on relatively small examples.