#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:  Implement
         Branch:                     |  backtracking properly
  u/SimonKing/ticket/15303           |       Commit:
   Dependencies:  #14711             |  74821fe5409c3104b5d6eb7407a8287d54170df9
                                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by SimonKing):

 * work_issues:  Analyse recursion error => Implement backtracking properly


Comment:

 In #12969, I fixed the backtracking algorithm for the discovery of
 actions. There, the problem was that the absence of an action was cached
 in the middle of backtracking, i.e., even though some paths were
 ''temporarily'' forbidden, so that an action was easily found after
 allowing the paths again.

 In the case of coerce maps, the backtracking algorithm is not properly
 implemented either. Namely, paths that have already been visited are not
 marked as "forbidden". I think this is a severe bug. It is amazing that it
 didn't show up before. In any case, it ''must'' be implemented here, since
 otherwise we will hardly be able to add the feature that this ticket is
 about.

--
Ticket URL: <http://trac.sagemath.org/ticket/15303#comment:49>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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