A fast implementation of polynomial factorization

Abstract

A new package for factoring polynomials with integer coefficients is described which yields significant improvements over previous implementations in both time and space requirements. For multivariate problems, the package features an inexpensive method for early detection and correction of spurious factors. This essentially solves the multivariate extraneous factor problem and eliminates the need to factor more than one univariate image, except in rare cases. Also included is an improved technique for coefficient prediction which is successful more frequently than prior versions at short-circuiting the expensive multivariate Hensel lifting stage. In addition some new approaches are discussed for the univariate case as well as for the problem of finding good integer substitution values. The package has been implemented both in Scratchpad II and in an experimental version of muMATH.