Computational aspects of Hensel-type univariate polynomial greatest common divisor algorithms

Abstract

Two Hensel-type univariate polynomial Greatest Common Divisor (GCD) algorithms are presented and compared. The regular linear Hensel construction is shown to be generally more efficient than the Zassenhaus quadratic construction. The UNIGCD algorithm for UNIvariate polynomial GCD computations, based on the regular Hensel construction is then presented and compared with the Modular algorithm based on the Chinese Remainder Algorithm. From both an analytical and an experimental point of view, the UNIGCD algorithm is shown to be preferable for many common univariate GCD computations. This is true even for dense polynomials, which was considered to be the most suitable case for the application of the Modular algorithm.