Moss, Aaron2023-03-012023-03-012012Thesis 9102https://unbscholar.lib.unb.ca/handle/1882/14398This thesis details a method of enumerating bases of hyperplane arrangements up to symmetries. I consider here automorphisms, geometric symmetries which leave the set of all points contained in the arrangement setwise invariant. The algorithm for basis enumeration described in this thesis is a backtracking search over the adjacency graph implied on the bases by minimum-ratio simplex pivots, pruning at bases symmetric to those already seen. This work extends Bremner, Sikiric, and Schiirmann's method for basis enumeration of polyhedra up to symmetries, including a new pivoting rule for finding adjacent bases in arrangements, a method of computing automorphisms of arrangements which extends the method of Bremner et al. for computing automorphisms of polyhedra, and some associated changes to optimizations used in the previous work. I include results of tests on ACEnet clusters showing an order of magnitude speedup from the use of C++ in my implementation, an up to 3x speedup with a 6-core parallel variant of the algorithm, and positive results from other optimizations.text/xmlviii, 69 pageselectronicen-CAhttp://purl.org/coar/access_right/c_abf2Hyperspace.Symmetry.Algorithms.Polyhedra.master thesis2023-03-01Bremner, David(OCoLC)1342601301Computer Science