Computing in arithmetic groups with Voronoï's algorithm
Langue
en
Article de revue
Ce document a été publié dans
Journal of Algebra. 2015-08-01, vol. 435, p. 263–285
Elsevier
Résumé en anglais
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 QQ. Our method is based on a generalisation of Voronoï's algorithm for computing ...Lire la suite >
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 QQ. Our method is based on a generalisation of Voronoï'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.< Réduire
Mots clés en anglais
Unit groups of orders
Generators
Presentation
Word problem
Lattices
Voronoï's algorithm
Origine
Importé de halUnités de recherche