find the train track map
Opened this issue · 6 comments
Given that we find the transition matrix, is is hard to find the actual train-track map?
See this folder for some notes.
We should be able to this by accumulating the map piece-by-piece in traintrack::fold. We need a way to label main and infinitesimal edges consistently (with orientation). That's probably already done in some way using the coding.
The positive edge orientation can be taken as that traversed by the coding?
Can use multigon_index and multigon_prong_index to label the infinitesimal edges around multigon.
Main idea: make a "free word" class (basically an ordered list). Derive from it main edges (numbered by some edge_index) and infinitesimal edges (numbered using a combination of multigon_index and multigon_prong_index.). The latter would also contain a way to print a string describing what they are, or a more cryptic number for storage.
Main problem is inverses... But ignore those for now.
See branch iss003-tt-map. I think I need to define "small" train track maps for each step (mappings of each generator to a word), which could then be applied successively, as in the notes.
Ok, getting closer in 3fe0a02! I can get the basic map from the matrices. Not 100% sure it's right, though. In particular I'm not sure I'm doing the right thing as far as orientation is concerned. Need to draw some examples.
I think I need to rewrite so that it uses recursion directly instead of guessing the tt map from the matrices. Then I can likely pick up the infinitesimal edges as I go.
TODO: Maybe write the ttmap equivalent of mathmatrix_permplus1.