#20154: train-tracks
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Reporter: dbenielli | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-7.1
Component: combinatorics | Resolution:
Keywords: free-group automorphisme | Merged in:
Authors: Dominique Benielli and | Reviewers:
Thierry Coulbois | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by {'newvalue': u'Dominique Benielli and Thierry Coulbois',
'oldvalue': ''}):
* keywords: => free-group automorphisme
* component: PLEASE CHANGE => combinatorics
* type: PLEASE CHANGE => task
* author: => Dominique Benielli and Thierry Coulbois
Old description:
New description:
We propose to implement in Sage the train-tracks package developped by
Thierry Coulbois:
The main feature and the main achievement of the program is to compute
train- track representative for (outer) automorphisms of free groups.
phi.train track() computes a train-track representative for the (outer)
automorphism phi. This train-track can be either an absolute train-track
or a relative train-track. The celebrated theorem of Bestvina and Feighn
[?] assures that if phi is fully irre- ducible (iwip) then there exists an
absolute train-track representing phi.
The train-track(relative=False) method will terminate with either an
absolute train-track or with a topological representative with a
reduction: an invariant strict subgraph with non-trivial fundamental
group.
One more feature of train-tracks (absolute or relative) is to lower the
number of Nielsn paths. Setting the stable=True option will return a
train-track with at most one indivisible Nielsen path (per exponential
stratum if it is a relative train-track).
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Ticket URL: <http://trac.sagemath.org/ticket/20154#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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