ModularGroup.m is a Mathematica package which has been developed in the course of the diploma thesis Computer Algebra and Analysis: Complex Variables Visualized [pdf], carried out at the Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz by Thomas Ponweiser under supervision of Univ.-Prof. Dr. Peter Paule.The main focus lies on the visualization of basic results in the context of the theory of the modular group and modular functions. Most importantly the package provides
A more detailed description of the package's features as well as several examples, including interactive demonstrations, can be found in the notebook ModularGroupDemo.nb.
- Basic operations related to Möbius transformations and modular transformations (such as function composition as well as mapping of points and generalized disks),
- Algorithms for finding group word representations of modular transformations in terms of different generators of the modular group,
- Routines for drawing the canonical fundamental region of the modular group and the induced tessellation of the upper half-plane (as well as Möbius-transformed images thereof).
The MIT License (MIT)
Copyright (C) 2014 Thomas Ponweiser
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The package For using the package, download the following file and put it into a directory where Mathematica will find it. For a description of the usage of the package, see the ModularGroupDemo.nb notebook and the Diploma Thesis of Thomas PonweiserPlease report any bugs or other suggestions to Thomas Ponweiser.