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The Origami Package

Computing Veech groups of origamis

Version 2.0.2

22 April 2026

Leo Emmerich
Email: leem00001@stud.uni-saarland.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html

Sebastian Engelhardt
Email: seen00001@stud.uni-saarland.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html

Simon Ertl
Email: s8siertl@stud.uni-saarland.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html

Luca L. Junk
Email: junk@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weber-moritz/team/luca-junk.html

Pascal Kattler
Email: kattler@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen/team/pascal-kattler.html

Alexander Rogovskyy
Email: s8alrogo@stud.uni-saarland.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html

Pascal Schumann
Email: s8pcschu@stud.uni-saarland.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html

Andrea Thevis
Email: thevis@math.uni-frankfurt.de
Homepage: https://www.uni-frankfurt.de/115635174/Dr__Andrea_Thevis

Hannah Wagmann
Email: wagmann@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen/team/hannah-wagmann.html

Gabriela Weitze-Schmithüsen
Email: weitze@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen/team/gabriela-weitze-schmithuesen.html

Copyright

© 2018-2026 by Leo Emmerich, Sebastian Engelhardt, Simon Ertl, Luca Junk, Pascal Kattler, Alexander Rogovskyy, Pascal Schumann, Andrea Thevis, Hannah Wagmann 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 Cyclic Torus Covers
5 Functions for Dessins d'enfants
6 More special Origamis
7 Sytoles of Translation Surfaces
References
Index

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