Efficient Finite Fields in the Maxima Computer Algebra System

Authors:
Fabrizio Caruso;Jacopo D'Aurizio;Alasdair Mcandrew
Affiliations:
Dipartimento di Matematica L. Tonelli, Università di Pisa, Pisa, Italy;Dipartimento di Matematica L. Tonelli, Università di Pisa, Pisa, Italy;School of Computer Science and Mathematics, Victoria University, Melbourne, Australia
Venue:
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Year:
2008

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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.