train-tracks - Githubissues

We propose to implement in Sage the train-tracks package developed 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 irreducible (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 Nielsen 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).

sagemath / sage

train-tracks #20154

31223: Add sage-train-track as an optional package