Nouvelle Cuisine for the Computation of the Annihilating Ideal of fs

Let f1,..., fp be polynomials in C[x1,..., xn] and let D = Dn be the n-th Weyl algebra. The annihilating ideal of $f^{s}=f_{1}^{s1}...f_{p}^{sp}$ in D[s]=D[s1,...,sp] is a necessary step for the computation of the Bernstein-Sato ideals of f1,..., fp. 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.

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