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The Origami Package

Computing Veech groups of origamis

Version 2.0.0

15.07.2022

Simon Ertl
Email: s8siertl@stud.uni-saarland.de
Homepage: http://www.math.uni-sb.de/ag/weitze/
Address:
AG Weitze-Schmithüsen
FR 6.1 Mathematik
Universität des Saarlandes
D-66041 Saarbrücken

Luca L. Junk
Email: junk@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weber-moritz/team/luca-junk.html
Address:
Saarland University
Department of Mathematics
Postfach 15 11 50
66041 Saarbrücken
Germany

Pascal Kattler
Email: kattler@math.uni-sb.de
Homepage: http://www.math.uni-sb.de/ag/weitze/
Address:
AG Weitze-Schmithüsen
FR 6.1 Mathematik
Universität des Saarlandes
D-66041 Saarbrücken

Alexander Rogovskyy
Email: s8alrogo@stud.uni-saarland.de
Homepage: http://www.math.uni-sb.de/ag/weitze/
Address:
AG Weitze-Schmithüsen
FR 6.1 Mathematik
Universität des Saarlandes
D-66041 Saarbrücken

Andrea Thevis
Email: thevis@math.uni-frankfurt.de
Homepage: https://www.uni-frankfurt.de/115635174/Dr__Andrea_Thevis
Address:
FB 12 - Institut für Mathematik
Johann Wolfgang Goethe-Universität
Robert-Mayer-Str. 6-8
D-60325 Frankfurt am Main

Gabriela Weitze-Schmithüsen
Email: weitze@math.uni-sb.de
Homepage: http://www.math.uni-sb.de/ag/weitze/
Address:
AG Weitze-Schmithüsen
FR 6.1 Mathematik
Universität des Saarlandes
D-66041 Saarbrücken

Copyright

© 2018-2022 by Simon Ertl, Luca Junk, Pascal Kattler, Alexander Rogovskyy, Andrea Thevis and Gabriela Weitze-Schmithüsen

Acknowledgements

We thank Sergio Siccha for his support and valuable input at the beginning of this project. Furthermore, we would like to thank Vincent Delecroix and Samuel Lelièvre for fruitful discussions about algorithms implemented in the surface_dynamics package in sage. Some of the functionality of the surface_dynamics package can be used in this package as well. For this we use an interface between GAP and sage. We are grateful to Mohamed Barakat and Markus Pfeiffer for helping teaching us how to use these interfaces. Moreover, we thank Thomas Breuer for helpful ideas and comments on some algorithms implemented in this package.

This software package is part of the project I.8 'Algorithmic approaches to Teichmüller curves' (AG Weitze-Schmithüsen, Saarland University) supported by SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German Research Foundation (DFG).

Contents

1 Introduction
2 The functionality of this package
3 The homology of origamis and the action of the Veech group.
4 SageMath and the surface_dynamics package
5 The Origami Database
6 Cyclic Torus Covers
7 More special Origamis
References
Index

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