#15303: Coercion discovery fails to be transitive
-------------------------------------+-------------------------------------
       Reporter:  nbruin             |        Owner:
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-5.13
      Component:  coercion           |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Simon King         |    Reviewers:
Report Upstream:  N/A                |  Work issues:  analyse recursion
         Branch:                     |  error
  u/SimonKing/ticket/15303           |       Commit:
   Dependencies:  #14711             |  f837cbee8f81c4946a92193c73e86449c53515d9
                                     |     Stopgaps:
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Comment (by SimonKing):

 Replying to [comment:27 SimonKing]:
 > 2. Let the user-provided morphism count for the number of morphisms
 found in `.discover_coercion()`. Hence, if `num_paths=1` and the user
 provides a morphism, then the maximal number of paths-to-be-considered is
 attained and hence the user-provided morphism is returned without
 backtracking.
 >
 > I think the second point is more important, and I will implement it now.

 Note one remark in the code:
 {{{
                 # If there is something better in the list, try to return
 that instead
                 # This is so, for example, _coerce_map_from_ can return
 True but still
                 # take advantage of the _populate_coercion_lists_ data.
 }}}
 The `_populate_coercion_lists_` data are also put into
 `_coerce_from_cache`. Hence, these data will have priority over
 `_coerce_map_from_` in `self.coerce_map_from(other)`. Therefore,
 `self.discover_coerce_map_from(other)` will ''only'' be called if there
 are no relevant `_populate_coercion_lists_` data.

 Hence, I believe that the remark is not valid, and will remove it.

--
Ticket URL: <http://trac.sagemath.org/ticket/15303#comment:29>
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