Implement tete-a-tete graphs

[sagetrac-pportilla]

In this ticket we will implement tete-a-tete graphs. These are ribbon graphs together with a metric on its edges satisfying a certain property (the tete-a-tete property). These are an original idea by the mathematician Norbert A'Campo in [A2009]. A tete-a-tete graph encodes the mapping class of an automorphism of a surface with boundary that restricts to the identity to the boundary of this surface and whose mapping class is periodic (when we allow isotopies to rotate the boundary components). Also some ideas were further developed by C. Graf, an student of A'Campo in [G2015]. Also, my current PhD thesis develops other aspects of these graphs.

These are some of the ideas that will be implemented in this ticket:

• A class of objects called TatGraph (tat stands for tete-a-tete). This includes the notion of relative tat graph, which are a kind of graphs that allow to permute certain boundary components of the thickening of the underlying ribbon graph.
• Numerous methods for the class above, for instance:
  • Rotation numbers around each boundary component
  • Matrix depicting the action on the first homology group of the ribbon graph with respect to the basis given by RibbonGraph.homology_basis()
  • Global method to find the end of a safewalk of a certain length.
  • Global method that produces examples of tat graphs. In particular it produces all Milnor fibers and monodromies of the Brieskorn-Pham singularities.
  • Orbit graph, this is a ribbon graph that corresponds to the orbit space resulting from taking the quotient of the original underlying ribbon graph by the action the the automorphism induced by the tat property.

[A2009] N. A'Campo, Tete-a-tete graphs and geometry monodromy.

[G2015] C.Graf, Tete-a-tete graphs and periodic automorphisms of surfaces.

CC: @tscrim @sagetrac-tmonteil

Component: geometry

Keywords: tat, ribbon graphs, tete-a-tete, periodic, automorphisms, surfaces, boundary

Author: Pablo Portilla

Branch/Commit: u/pportilla/tat_graph-22016 @ b3fb968

Issue created by migration from https://trac.sagemath.org/ticket/22016

[sagetrac-pportilla]

Changed branch from public/geometry/tat_graphs to u/pportilla/tat_graphs

[sagetrac-pportilla]

Changed branch from u/pportilla/tat_graphs to u/pportilla/tat_graph

[sagetrac-pportilla]

Changed author from Pablo Portilla to pportilla

[sagetrac-pportilla]

comment:5

I just created this ticket from the web interface but I can't checkout on it from the console in my compute by doing "git trac checkout 22016", it returns:

Loading ticket #22016...
Checking out Trac #22016 remote branch u/pportilla/tat_graph -> local branch t/22016/tat_graph...
Traceback (most recent call last):
File "/usr/local/bin/git-trac", line 18, in
cmdline.launch()
File "/usr/local/lib/python2.7/dist-packages/git_trac/cmdline.py", line 215, in launch
app.checkout(args.ticket_or_branch, args.branch_name)
File "/usr/local/lib/python2.7/dist-packages/git_trac/app.py", line 116, in checkout
self._checkout_ticket(int(ticket_or_branch), branch_name)
File "/usr/local/lib/python2.7/dist-packages/git_trac/app.py", line 144, in _checkout_ticket
self.repo.checkout_new_branch(ticket.branch, branch)
File "/usr/local/lib/python2.7/dist-packages/git_trac/git_repository.py", line 136, in checkout_new_branch
self.git.fetch('trac', remote)
File "/usr/local/lib/python2.7/dist-packages/git_trac/git_interface.py", line 341, in meth
return self.execute(git_cmd, *args, **kwds)
File "/usr/local/lib/python2.7/dist-packages/git_trac/git_interface.py", line 328, in execute
popen_stderr=subprocess.PIPE)
File "/usr/local/lib/python2.7/dist-packages/git_trac/git_interface.py", line 263, in _run
raise GitError(result)
git_trac.git_error.GitError: git returned with non-zero exit code (128) when executing "git fetch trac u/pportilla/tat_graph"
STDERR: fatal: Couldn't find remote ref u/pportilla/tat_graph
STDERR: fatal: The remote end hung up unexpectedly

I can, however fetch other tickets like for example 21587. Any ideas?

[sagetrac-pportilla]

Changed branch from u/pportilla/tat_graph to u/pportilla/tat_graph-22016

[tscrim]

comment:8

Were you able to fix the git trac command issue? If not, have you tried using git directly?

[tscrim]

Changed author from pportilla to Pablo Portilla

[sagetrac-pportilla]

comment:9

Replying to @tscrim:

Were you able to fix the git trac command issue? If not, have you tried using git directly?

No I haven't been able to solve it and yes, I have also tried "git fetch -v trac u/pportilla/tat_graph-22016 && echo OK" and it returns the same kind of error " fatal: Couldn't find remote ref u/pportilla/tat_graph-22016"

I can checkout other tickets so I don't know what can be the problem.

[tscrim]

comment:10

Can you send me the results of git remote -v to my e-mail (tscrimsh at umn * edu, with * = dot)?

[sagetrac-git]

Commit: 87e3342

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

4cd202e	Suggested changes commited
72ef663	Fixed similar lines and turned them more "pythonic"
f4a419c	Merge branch 'u/pportilla/ribbon_graphs' of trac.sagemath.org:sage into public/geometry/ribbon_graphs-21587
6b0f5fc	Reworking some things with the documentation and internal structures.
4e3b676	Added extra test to _find.
0075562	Added one method and one function. Both were already included in the next work I will be uploading when this is positively reviewed, but since they refer strictly to ribbon graphs I think that they suit better here.
6f4b8a6	Added a missing example.
82b52eb	Fixed typos and normalized name of method.
b22ef55	Merge branch 'public/geometry/ribbon_graphs-21587' of trac.sagemath.org:sage into public/geometry/ribbon_graphs-21587
87e3342	Moving the bipartite construction into the RibbonGraph constructor.

[sagetrac-pportilla]

comment:12

I just updated the branch with all the commits from #21587 (since it depends on it)

[sagetrac-git]

Changed commit from 87e3342 to af006ae

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

af006ae

Included main file and changes so that I can start trying compilation.

[sagetrac-git]

Changed commit from af006ae to 7d46117

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7d46117

silly mistake on the lazy imports

[sagetrac-git]

Changed commit from 7d46117 to 8088978

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

809412e	fixed indentation on docstring
f8339da	Included main file and changes so that I can start trying compilation.
8088978	silly mistake on the lazy imports

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6dbbf00	Merge branch 't/22016/tat_graph-22016' into develop
ec1b5a2	Merge branch 'develop' into t/22016/tat_graph-22016

[sagetrac-git]

Changed commit from 8088978 to ec1b5a2

[tscrim]

comment:17

Is this ready for review?

[sagetrac-pportilla]

comment:18

Replying to @tscrim:

Is this ready for review?

Hi. No, it is not. I have been busy. This is my last PhD year and, as you can imagine, I lack of time. Nevertheless, I will be back on this soon (I hope).

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5011758

Forgot to run docbuild and produced some errors, now fixed.

[fchapoton]

comment:46

(1) This is not the right way:

while (finish_cycle == False):

should rather be

while not finish_cycle:

(2) idem here

while (len(aux_orbits_rho) > 0):

could be

while aux_orbits_rho:

(3)
This

+    darts = [x for i in range(len(aux_sigma)) for x in aux_sigma[i]]

could be

darts = [x for y in aux_sigma for x in y]

(4)
This

+    for i in range(len(aux_sigma[orb_vertex[0]])):
+        assert tat_graph._metric[aux_sigma[orb_vertex[0]][i]] > epsilon

could be

+    for y in aux_sigma[orb_vertex[0]]:
+        assert tat_graph._metric[y] > epsilon

[tscrim]

comment:47

I just want to expand slightly on (1) that there are a few places where you are checking if foo == True:/if foo == False: and all of those should be changed appropriately to ``if foo:/if not foo:`.

[sagetrac-git]

Changed commit from 5011758 to ee1c35b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ee1c35b

More examples, cleaning code in the direction indicated.

[sagetrac-git]

Changed commit from ee1c35b to b3fb968

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b3fb968

A couple more of changes suggested by tscrim

[fchapoton]

comment:50

This has not been corrected:

while (len(darts) > 0):

[fchapoton]

comment:51

and the branch is now red, meaning some conflicts with the latest develop version of sage

[mkoeppe]

comment:54

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

comment:55

Setting a new milestone for this ticket based on a cursory review.