Zero testing of p-adic and modular polynomials

We obtain new algorithms for testing whether a given by a black box multiva riate polynomial over p-adic fields given by a black box is identical to ze ro. We also remark on the zero testing of polynomials in residue rings. Our results complement a known results on the zero testing of polynomials over the integers, the rationals, and over finite fields. (C) 2000 Elsevier Sci ence B.V. All rights reserved.