A simple algorithm for GCD of polynomials - Nardone, Pasquale; Sonnino, Giorgio (Annals of Mathematics and Physics, 2022)
Based on the Bezout approach we propose a simple algorithm to determine the gcd of two polynomials that don’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 or determinant calculation.