Nouvelle Cuisine for the Computation of the Annihilating Ideal of $f^s$

Abstract

Let $f_1,\ldots, f_p$ be polynomials in ${\bf C}[x_1,\ldots, x_n]$ and let $D = D_n$ be the $n$-th Weyl algebra. The annihilating ideal of $f^s=f_1^{s_1}\cdots f_p^{s_p}$ in $D[s]=D[s_1,\ldots,s_p]$ is a necessary step for the computation of the Bernstein-Sato ideals of $f_1,\ldots, f_p$.

We point out experimental differences among the efficiency of the available methods to obtain this annihilating ideal and provide some upper bounds for the complexity of its computation.