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Congruence

Congruence subgroups of SL_2(ℤ)

Version 1.1.1

28 October 2014

Ann Dooms
Email: andooms@vub.ac.be
Homepage: http://homepages.vub.ac.be/~andooms
Address:
Department of Mathematics, Vrije Universiteit Brussel
Pleinlaan 2, Brussels, B-1050 Belgium

Eric Jespers
Email: efjesper@vub.ac.be
Homepage: http://homepages.vub.ac.be/~efjesper
Address:
Department of Mathematics, Vrije Universiteit Brussel
Pleinlaan 2, Brussels, B-1050 Belgium

Alexander Konovalov
Email: alexk@mcs.st-andrews.ac.uk
Homepage: http://www.cs.st-andrews.ac.uk/~alexk/
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Helena Verrill
Email: verrill@math.lsu.edu
Homepage: http://www.math.lsu.edu/~verrill/
Address:
Department of Mathematics
Louisiana State University
Baton Rouge, Louisiana, 70803-4918
USA

Abstract

The GAP package Congruence provides functionality to work with congruence subgroups of SL_2(ℤ).

Copyright

© 2006-2014 by Ann Dooms, Eric Jespers, Alexander Konovalov and Helena Verrill.

Congruence is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF's own site http://www.gnu.org/licenses/gpl.html.

If you obtained Congruence, we would be grateful for a short notification sent to one of the authors.

If you publish a result which was partially obtained with the usage of Congruence, please cite it in the following form:

A. Dooms, E. Jespers, A. Konovalov and H. Verrill. Congruence --- Congruence subgroups of SL_2(ℤ), Version 1.1.1; 2014 (http://www.cs.st-andrews.ac.uk/~alexk/congruence/).

Acknowledgements

We are very grateful to Mong-Lung Lang, Chong-Hai Lim and Ser Peow Tan for their comments provided while implementing algorithms from [LLT95a] and [LLT95b], and to Francqui Stichting (Belgium) for the support of the third author.

Contents

1 Introduction
2 Construction of congruence subgroups
3 Farey symbols and their properties
4 Farey symbols for congruence subgroups
5 Service functions of the Congruence package
References
Index

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