Implementing a polynomial factorization and GCD package

Abstract

This paper describes the construction of a rational function package where the GCD and factorization routines are well integrated and consistent with each other and both use state of the art algorithms. The work represents an exercise in producing a service rather than an experimental piece of code, where portability, reliability and clear readable code are important aims in addition to the obvious desire for speed. Measurements on the initial version of our package showed that even though it was based on the best of previously published methods its performance was uneven. The causes of the more notable bottle necks and the steps we took to avoid them are explained here and illustrate how apparently very fine details of coding can sometimes have gross effects on a system's overall behaviour.