The EEZ-GCD algorithm

Abstract

An enhanced gcd algorithm based on the EZ-GCD algorithm is described. Implementational aspects are emphasized. It is generally faster and is particularly suited for computing gcd of sparse multivariate polynomials. The EEZ-GCD algorithm is characterized by the following features:(1) avoiding unlucky evaluations,(2) predetermining the correct leading coefficient of the desired gcd,(3) using the sparsity of the given polynomials to determine terms in the gcd and(4) direct methods for dealing with the "common divisor problem." The common divisor problem occurs when the gcd has a different common divisor with each of the cofactors. The EZ-GCD algorithm does a square-free decomposition in this case. It can be avoided resulting in increased speed. One method is to use parallel p-adic construction of more than two factors. Machine examples with timing data are included.