Authors: Luca De Feo, Javad Doliskani and Éric Schost

We present algorithms to construct and do arithmetic operations in the algebraic closure of the finite field GF(p). Our approach is inspired by algorithms for constructing irreducible polynomials, which first reduce to prime power degrees, then use composita techniques. We use similar ideas to give efficient algorithms for embeddings and isomorphisms.

Notice: this is the authors' version of the work presented at the International Symposium on Symbolic and Algebraic Computation 2014 in Kobe. It is posted here by permission of ACM for your personal use, which arguably includes your right to fork this repository. A proceedings-frozen version was published in the Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, pages 122-129, http://dx.doi.org/10.1145/2608628.2608672, but the paper keeps evolving!

This repository contains the LaTeX source code of the paper, the code used for testing purposes, and some more C code giving a proof-of-concept. The Sage tests must be run against the experimental branch hosted at https://github.com/defeo/sage/tree/ff_compositum.