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Modeling Finite Fields with Mathematica. Applications to the Computation of Exponential Sums and to the Solution of Equations over Finite Fields

A. Vantaggiato
Journal / Anthology

Lecture Notes in Computer Science
Year: 1993
Volume: 722
Page range: 364-368

This paper proposes an implementation model for finite fields GF[mq], m prime, based on a hybrid architecture that integrates symbolic programming developed in Mathematica with an imperative C language module. Its aim is to enable the user to write algorithms to perform calculations in GF's by using Mathematica's programming language and built-in math functions. First, the system's architecture is presented and it is shown that the proposed model has linear time complexity (O(q)) for all algebraic operations. Finally, we show the developed modules for the computation of exponential sums and the solution of equations over finite fields.

*Applied Mathematics > Computer Science
*Mathematics > Algebra > Field and Ring Theory