On Testing for Zero Polynomials by a Set of Points with Bounded Precision

Authors:
Jin-yi Cai;Eric Bach
Affiliations:
-;-
Venue:
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Year:
2001

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Abstract

We consider a general methodology proposed by Chen and Kao [4] for testing polynomial identities.We prove that the test cannot be completely derandomized by any specified set of rational approximations to algebraic numbers up to a polynomial number of bits. The proof is a direct application of Dirichlet's box principle. We also give some number theoretic estimates for the likelihood of a multiplicatively independent sequence of integers which can be used in their algorithm.