Efficient finite fields in the Maxima computer algebra system

Abstract

In this paper we present our implementation of finite fields in the free and open Maxima computer algebra system. In the first version of our package we focused our efforts on efficient computation of primitive elements and modular roots. Our optimizations involve some heuristic methods that use "modular composition" and the generalized Tonelli-Shanks algorithm. Other open and free systems such as GP/Pari do not include in their standard packages any support for finite fields. The computation of the primitive element in Maxima is now faster than in Axiom. Our package provides a more user-friendly interface for teaching than other comparable systems. © 2008 Springer-Verlag Berlin Heidelberg.