#16976: Conjugacy classes and rational period functions for Hecke triangle 
groups
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       Reporter:  jj                 |        Owner:
           Type:  enhancement        |       Status:  needs_info
       Priority:  major              |    Milestone:  sage-6.5
      Component:  modular forms      |   Resolution:
       Keywords:  hecke triangle     |    Merged in:
  group conjugacy class rational     |    Reviewers:
  period function                    |  Work issues:
        Authors:  Jonas Jermann      |       Commit:
Report Upstream:  N/A                |  3c7ca0f2bf33d3fdec7b79c353b28ccc01cd419d
         Branch:                     |     Stopgaps:
  u/jj/triangle_conjugacy            |
   Dependencies:  #16936             |
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Changes (by vdelecroix):

 * status:  needs_review => needs_info


Comment:

 Hi,

 It is standard in Sage to have documentation directly attached to the
 objects. If there is a need for a larger document that would serve as
 explanation or tutorial, then it is fine. But it is not where the main
 documentation should be. Moreover, such document should be listed in the
 "Thematic tutorials".

 I am still not happy with the `cached_method`. If it is long to compute
 the decomposition into generators from the matrix, then do not make it
 appear in `_repr_`. It is a nonsense to argue that some methods must be
 cached because of `__repr__`. Either this decomposition is important for
 computations, in which case it must be computed at the creation (and in
 parallel with the matrix multiplication). Or it is not, in which case it
 does not matter that it is long to compute. This concerns `_basic_data`
 and `_primitive_bloc_data`. On the other hand, why `continued_fraction` is
 still cached?

 If the information contained in `_basic_data`, `_primitive_bloc_data` and
 `_continued_fraction` are approximately equivalent, you can choose one of
 them for being cached. From what I understand:
 - `_primitive_block_data`: built from `continued_fraction`
 - `_block_data`: generalization of `_primitive_block_data`
 so there is for sure no need to cache all of them. And using
 `UniqueRepresentation` for elements is a bad idea (it will cost too much).

 line 2700
 {{{
         .. TODO:

           Improve the documentation!
 }}}
 Who will do that?

 I do have plenty of other remarks that I can partly implement myself. But
 I want the one above to be settled before going further.

 Vincent

--
Ticket URL: <http://trac.sagemath.org/ticket/16976#comment:24>
Sage <http://www.sagemath.org>
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