Basis enumeration of hyperplane arrangements up to symmetries

Given a symmetry group acting on the hyperplanes of an arrangement, our goal is to report a single basis from each orbit of bases induced by this group. In this paper we extend previous techniques for finding the (feasible) bases of polyhedra up to symmetry, and for computing the symmetry groups of polyhedra, to the setting of hyperplane arrangements. We present some preliminary experiments with a C++ implementation of these techniques called …