Deterministic identity testing for multivariate polynomials

Authors:
Richard Lipton;Nisheeth Vishnoi
Affiliations:
Georgia Institute of Technology, Atlanta GA;Georgia Institute of Technology, Atlanta GA
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

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Abstract

In this paper we present a simple deterministic algorithm for testing whether a multivariate polynomial f(x1, ..., xn) is identically zero, in time polynomial in m, n, log(d + 1) and H. Here m is the number of monomials in f, d is the maximum degree of a variable in f and 2H is the least upper bound on the magnitude of the largest coefficient in f. We assume that f has integer coefficients.The main feature of our algorithm is its conceptual simplicity. The proof uses Linnik's Theorem which is a deep fact about distribution of primes in an arithmetic progression.