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

摘要

Let $f_1,ldots, f_p$ be polynomials in ${f C}[x_1,ldots, x_n]$and let $D = D_n$ be the $n$-th Weyl algebra. The annihilatingideal 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 computationof the Bernstein-Sato ideals of $f_1,ldots, f_p$.We point out experimental differences among the efficiency of theavailable methods to obtain this annihilating ideal and providesome upper bounds for the complexity of its computation.