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

摘要

Let f_1,..., f_p be polynomials in C[x_1,..., x_n] and let D = D_n be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of f~s = f~(s_1)_1...f~(s_p)_p in D[s] = D[s_1, ..., s_p]. These bounds provide an initial explanation of the differences between the running times of the two methods known to obtain the so-called Bernstein-Sato ideals.