Computing in arithmetic groups with Voronoi's algorithm
Number Theory
2014-07-24 v1 Group Theory
Abstract
We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalisation of Vorono\"i's algorithm for computing perfect forms, combined with Bass-Serre theory. It differs essentially from previously known methods to deal with such questions, e.g. for units in quaternion algebras. We illustrate this new algorithm by a series of examples where the computations are carried out completely.
Cite
@article{arxiv.1407.6234,
title = {Computing in arithmetic groups with Voronoi's algorithm},
author = {Oliver Braun and Renaud Coulangeon and Gabriele Nebe and Sebastian Schoennenbeck},
journal= {arXiv preprint arXiv:1407.6234},
year = {2014}
}