Train-tracks for sage

By Thierry Coulbois

This is a webpage for my program that deals with (outer) automorphisms of free groups and computes train-track representative.


Getting started

All files and documents under Creative Commons Attribution 3.0 license. You are free to share, remix and make commercial use provided that you clearly attribute Sage.

It is now distrubuted as a python package on So just run Sage with
	sage -pip install train_track
Or if you do not have enough privileges
	sage -pip install --user train_track
Alternatively to bypass the access to internet, you can download the tarball from and install
	sage -pip install /path/to/train_track-0.1.2.tar.gz

See also the README.rst file, or alternatively the github repository:

We also plan to include it inside the standard Sage distribution and there is a ticket (#20154) at the Sage development web site. Please volunteer to review that ticket.

After installing usage is very easy:

	  sage: from train_track import *

  1. To use my package you need Sage.
    Sage is an open-source math-oriented software. It is highly recommended in everyday life of the working mathematician, both for teaching and research. Sage is very easy to install.
  2. Sage offers online help by using the key <tab> after the name of a variable followed by a dot or after an opening parenthesis.


Currently with my software you can work with:


TODO list

If there are volunteers to code new features or fix bugs...
Possible mathematic extensions Known bugs and weakness
  1. Fixed subgroup of an automorphism.
  2. Suggestions welcome.
  1. LaTeX output are not fully available.
  2. Conflict with the present FreeGroup of Sage (which is a wrapper of GAP). See ticket #20154
If you wish to contribute or get the most recent files, go to the github repository.

I am eager to get some feedback on my work. Please e-mail me comments, bug-reports, expectations, etc.: .