On testing for zero polynomials by a set of points with bounded precision

Authors:
Jin-Yi Cai;Eric Bach
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison, WI and Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY;Computer Sciences Department, University of Wisconsin, Madison, WI
Venue:
Theoretical Computer Science - Computing and combinatorics
Year:
2003

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Abstract

We consider a general methodology proposed by Chen and Kao 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.