Algorithm for Computing Bernstein-Sato Ideals Associated with a Polynomial Mapping

Let n, p be two strictly positive integers, and let f1(x), . . . , fp(x) ∈ K[x] := K[x1, . . . , xn] be p polynomials of n variables with coefficients in a fieldK of characteristic zero. Denote by An = K[x1, . . . , xn]〈∂x1 , . . . , ∂xn〉 the Weyl algebra with n variables and let s1, . . . , sp be new variables. Denote by L = K[x][f−1 1 , . . . , f−1 p , s1, . . . , sp] · f the free module generated by the symbol f where f is a notation for f1 1 · · · f sp p . L has a natural An[s]-module structure where An[s] := An[s1, . . . , sp]. We have, for instance: