Computational Higher Algebra
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Abstract
Some modern approaches to algebraic topology and quantum information make use of compound structures, such as matrices of matrices of complex numbers, which have a rich and beautiful theory. We have a computer algebra system written in Mathematica to help us manipulate these structures, but there are many gaps, and much scope for finding ingenious algorithms to improve performance. This project involves looking at the existing code (which is really quite simple!), understanding the mathematical problems it is solving, and working out how to do things better. Alternatively, there are opportunities to implement new and exciting features. There are many directions in which this project could be taken. The emphasis can be shifted depending on the student; it is appropriate for students interested in algorithms, rewriting, topology, or quantum information.