Connections Among Applied Computational Group Theory, Matrix Representations, and Parallel Computations

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The goals of this project are: (a) application of computational group theory to related areas, and (b) scalability of applications through parallelism. This is expected to be useful in areas of application including aspects of linear numerical analysis, search (especially in the presence of symmetry) and algorithmic parallelization. This work will take advantage of a sizable body of more mature and stable algorithms of computational group theory that has evolved in recent years. As an example, the techniques for finding invariant subspaces of matrices over finite fields (the meataxe and condensation) have matured in recent years, while invariant subspace techniques are of current interest for iterative techniques in numerical analysis. The relevant algorithms will be adapted to larger scale applications through the use of parallelism and of data structures adapted toward that parallelism. The TOP-C parallel methodology will be used to identify central, repetitive tasks. The portability of this methodology across C, LISP, GAP and other languages helps eliminate the continuing barriers to extensive use of parallelization.