Deterministic identity testing for multivariate polynomials

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.

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Richard J. Lipton, Nisheeth K. Vishnoi
• Keywords: Algorithms, Multivariate Polynomial, Simple Deterministic Algorithm, SODA 2003, Time Polynomial