Simple Algorithm for GCD of Polynomials

Abstract

Based on the Bezout approach we propose a simple algorithm to determine the gcd of two polynomials which doesn’t need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only n steps for polynomials of degree n. Formal manipulations give the discriminant or the resultant for any degree without needing division nor determinant calculation.