Doctor of Philosophy
Eric Schost and Jan Minac
We present algorithms to construct and perform computations in algebraic closures of finite fields. Inspired by algorithms for constructing irreducible polynomials, our approach for constructing closures consists of two phases; First, extension towers of prime power degree are built, and then they are glued together using composita techniques. To be able to move elements around in the closure we give efficient algorithms for computing isomorphisms and embeddings. In most cases, our algorithms which are based on polynomial arithmetic, rather than linear algebra, have quasi-linear complexity.
Doliskani, Javad, "Computing in Algebraic Closures of Finite Fields" (2015). Electronic Thesis and Dissertation Repository. 3282.