Factorization of multivariate polynomials by extended Hensel construction

Abstract

The extended Hensel construction is a Hensel construction at an unlucky evaluation point for the generalized Hensel construction, and it allows as to avoid shifting the origin in multivariate polynomial factorization. We have implemented a multivariate factorization algorithm which is based on the extended Hensel construction, by solving a leading coefficient problem which is peculiar to our method. We describe the algorithm and present some experimental results. Experiments show that the extended Hensel construction is quite useful for factoring multivariate polynomials which cause large expression swell by shifting the origin.