#18021: gyration orbits method for AlternatingSignMatrix and add optional 
parameter
for gyration method.
-------------------------------------+-------------------------------------
       Reporter:  egunawan           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.6
      Component:  combinatorics      |   Resolution:
       Keywords:  days64, gyration,  |    Merged in:
  alternating sign matrix            |    Reviewers:  Jessica Striker,
        Authors:  Emily Gunawan,     |  Travis Scrimshaw, James Propp
  Travis Scrimshaw                   |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  52705536f95a497f1573665374c75b69f5d9037f
  u/egunawan/ticket/18021            |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by tscrim):

 Here are my comments:

 - I don't like the `count` option to `gyration`. You are much better
 writing a simple `for` loop which applies the sequence of gyrations to
 avoid the unnecessary complexity.
 - Rename `obtain_gyration_orbit` to `gyration_orbit`.
 - Use `@cached_method` for `gyration_orbits` (and you should not say
 anything about its internal representation). Also have it return a tuple
 instead of a list.
 - Don't cache `gyration_orbit_sizes` since the previous caching will keep
 this fast (and definitely do not hardcode them).

 Also, do you want this to depend on #17988? If so, I should be able to do
 that review this week.

--
Ticket URL: <http://trac.sagemath.org/ticket/18021#comment:8>
Sage <http://www.sagemath.org>
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