On the complexity of computing the greatest common divisor of several univariate polynomials

Abstract

This paper is devoted to present a deterministic algorithm computing the greatest common divisor of several univariate polynomials with coefficients in an integral domain with the best known complexity bound when integer coefficients are considered. More precisely, if n is a bound for the degree of the t+1 integer polynomials whose greatest common divisor is to be computed and M is a bound for the size of those polynomials then such greatest common divisor is computed by means of O(tn 3) arithmetic operations involving integers whose size is in O(n 4 M) (which is independent of t).