#15303: Coercion discovery fails to be transitive
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       Reporter:  nbruin    |        Owner:
           Type:  defect    |       Status:  new
       Priority:  major     |    Milestone:  sage-5.13
      Component:  coercion  |   Resolution:
       Keywords:            |    Merged in:
        Authors:            |    Reviewers:
Report Upstream:  N/A       |  Work issues:
         Branch:            |       Commit:
   Dependencies:            |     Stopgaps:
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Comment (by SimonKing):

 I was thinking about "versioning" of the coercion graph as well. Perhaps
 it would be worth trying.

 The idea would be: We have one global variable, say, `cdef unsigned int
 coerce_graph_version`. Whenever we create a node that is neither a sink
 nor a source in the coerce graph, we increment the variable. This would be
 cheap, a simple test in `.register_coercion()` and
 `.register_embedding()`.

 Instead of storing `None` when a coercion can not be found, we store the
 current version. Hence, if we do `mor = self._coerce_from_hash[P]`, a
 simple `isinstance(mor,int)` (or a faster version from the Python API that
 tests if the type of `mor` is ''exactly'' `int`) will tell us whether the
 absence of a coercion was cached. If `mor==coerce_graph_version` then we
 know that the cached absence of a coercion is reliable. Otherwise, we need
 to test.

 Would this really be soooo expensive? I don't think so. Of course, it
 depends on how often we create non-sink non-source nodes---and I doubt
 that the combined use of `.register_embedding()` and
 `.register_coercion()` (which is the only way to create non-sink non-
 source) will happen very often.

 So, I'd say we simply try.

--
Ticket URL: <http://trac.sagemath.org/ticket/15303#comment:4>
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