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Full-Text Articles in Algebra
A Generic Implementation Of Fast Fourier Transforms For The Bpas Library, Colin S. Costello
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 …
Equivariant Cohomology For 2-Torus Actions And Torus Actions With Compatible Involutions, Sergio Chaves Ramirez
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 …