Digital Commons Network^™

Applying Front End Compiler Process To Parse Polynomials In Parallel, Amha W. Tsegaye

Electronic Thesis and Dissertation Repository

Parsing large expressions, in particular large polynomial expressions, is an important task for computer algebra systems. Despite of the apparent simplicity of the problem, its efficient software implementation brings various challenges. Among them is the fact that this is a memory bound application for which a multi-threaded implementation is necessarily limited by the characteristics of the memory organization of supporting hardware.

In this thesis, we design, implement and experiment with a multi-threaded parser for large polynomial expressions. We extract parallelism by splitting the input character string, into meaningful sub-strings that can be parsed concurrently before being merged into a single …

A Generic Implementation Of Fast Fourier Transforms For The Bpas Library, Colin S. Costello

Electronic Thesis and Dissertation Repository

In this thesis we seek to realize an efficient implementation of a generic parallel fast Fourier transform (FFT). The FFT will be used in support of fast multiplication of polynomials with coefficients in a finite field. Our goal is to obtain a relatively high performing parallel implementation that will run over a variety of finite fields with different sized characteristic primes. To this end, we implement and compare two Cooley-Tukey Six-Step fast Fourier transforms and a Cooley-Tukey Four-Step variant against a high performing specialized FFT already implemented in the Basic Polynomial Algebra Subprograms (BPAS) library. We use optimization techniques found …

Locally Persistent Categories And Metric Properties Of Interleaving Distances, Luis N. Scoccola

Electronic Thesis and Dissertation Repository

This thesis presents a uniform treatment of different distances used in the applied topology literature. We introduce the notion of a locally persistent category, which is a category with a notion of approximate morphism that lets one define an interleaving distance on its collection of objects. The framework is based on a combination of enriched category theory and homotopy theory, and encompasses many well-known examples of interleaving distances, as well as weaker notions of distance, such as the homotopy interleaving distance and the Gromov–Hausdorff distance.

We show that the approach is not only an organizational tool, but a useful theoretical …

Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, Sergio Chaves Ramirez

Electronic Thesis and Dissertation Repository

The Borel equivariant cohomology is an algebraic invariant of topological spaces with actions of a compact group which inherits a canonical module structure over the cohomology of the classifying space of the acting group. The study of syzygies in equivariant cohomology characterize in a more general setting the torsion-freeness and freeness of these modules by topological criteria. In this thesis, we study the syzygies for elementary 2-abelian groups (or 2- tori) in equivariant cohomology with coefficients over a field of characteristic two. We approach the equivariant cohomology theory by an equivalent approach using group cohomology, that will allow us to …