Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials

Let f1, . . . , fp be polynomials in C[x1, . . . , xn] and let D = Dn be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of f s = f s1 1 · · · f sp p in D[s] = D[s1, . . . , sp]. These bounds provide an initial explanation on the differences between the running times of the two methods known to obtain the so-called BernsteinSato ideals.Ministerio de Ciencia y Tecnología MTM2004-01165Junta de Andalucía FQM-33