#18756: Use coerce actions in the category framework
-------------------------------------+-------------------------------------
       Reporter:  SimonKing          |        Owner:
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.8
      Component:  coercion           |   Resolution:
       Keywords:  cython, coercion,  |    Merged in:
  actions, categories                |    Reviewers:  Travis Scrimshaw
        Authors:  Simon King         |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  a5bdbf6f85ea0d732a13ebc7d8e91dbd28c92ef0
  u/SimonKing/combinatorial_free_module_cython_coercion|     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by SimonKing):

 Meanwhile I think it is essential to ascend the MRO resp. the category
 hierarchy.

 Rationale: The plan for #18758 is to let `Magmas().parent_class` provide a
 `_get_action_` method returning a multiplicative action of self on self,
 while `AdditiveMagmas().parent_class._get_action_` yields an additive
 action of self on self. Hence, in order to get a ring structure, it is
 essential that `Parent.get_action` has access to both categorical
 `_get_action_` methods.

 To be fixed (here or in #18758?) is the issue with wrongly initialised
 parents. By this, I mean `isinstance(P, C.parent_class) and not
 isinstance(P, P.category().parent_class)` for a proper super-category C of
 `P.category()`.

 One could easily work around, but this would involve a little slow-down.
 So, better fix the issue rather than working around!

--
Ticket URL: <http://trac.sagemath.org/ticket/18756#comment:40>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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