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
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
It is now distrubuted as a python package on pypi.python.org. 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 pypi.python.org/simple/train_track and install
sage -pip install /path/to/train_track-0.1.2.tar.gz
See also the README.rst file, or alternatively
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 *
- 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.
- Sage offers online help by using the key
<tab> after the name of
a variable followed by a dot or after an opening parenthesis.
Overview Currently with my software you can work with:
- Free group automorphisms: apply to words, composition, inverse;
there are predefined automorphisms: Dehn twists, surface Dehn twists,
braids, and a list of examples from the litterature.
- Random automorphisms (or mapping classes or braids)
allowing statistical and asymptotic tests and conjectures.
- Topological representatives: these are graphs together with a
marking and a homotopy equivalence. the rose representative of an
automorphism is defined. You can fold, fusion edges, contract
invariant forests and tails, etc.
- Train-tracks: This is the main achievement of my program: it
computes train-track representatives: absolute train-tracks if any,
stable train-tracks (i.e. with at most one essential indivisible
Nielsen path (INP)), relative train-tracks and stable relative
train-tracks. Finds INP.
- Decide wether an automorphism is fully irreducible (iwip).
- Compute the index, index list and ideal Whitehead graphs.
- Most methods have a
- Construct Guirarderl's Convex Core for two simplicial trees in Outer Space and its boundary.
- [11 mars 2021] Ubuntu 20.04.2, Sage 9.2, train_track-0.1.3 failing badly due to changes in the wrapping of GAP FreeGroup into Sage
- [11 mars 2021] Ubuntu 20.04.2, Sage 9.0, train_track-0.1.3 all tests pass
- [13 mai 2019] deprecation of generic_power() between sage 8.1 and sage 8.2, creates some bugs with powers of automorphisms with sage less ore equal to 8.1.
- [21 mars 2018]
Ubuntu 16.04 and Sage 8.1: all tests pass (but 1 fail in ConvexCore)
- [24 avril 2018]MacBook Pro (13 pouces, mi-2012), Mac OS 10.13.4 and Sage 8.1: all tests pass.
If there are volunteers to code new features or fix bugs...
If you wish to contribute or get the most recent files, go to the github repository.
|Possible mathematic extensions
||Known bugs and weakness|
- Fixed subgroup of an automorphism.
- Suggestions welcome.
- LaTeX output are not fully available.
- Conflict with the present FreeGroup of Sage (which is a
wrapper of GAP). See ticket #20154
I am eager to get some feedback on my work. Please e-mail me
comments, bug-reports, expectations,