#16651: Buggy to_poly_solve option
-------------------------------------+-------------------------------------
       Reporter:  gagern             |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  critical           |    Milestone:  sage-6.3
      Component:  symbolics          |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Volker Braun       |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/vbraun/buggy_to_poly_solve       |  2573b80af24cf5938c089758dff7304ca53c9569
   Dependencies:                     |     Stopgaps:
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Comment (by gagern):

 I guess it might be next week before I find the time to have a closer look
 at this. And I don't know the code in this area, and have little
 experience with Maxima itself either. In any case, would I be correct to
 assume that `options='algexact:true'` is the critical point here?

 Notes to self or any other reviewer:
 * Omitting `multiplicities` in the condition makes sense, since
 `to_poly_solve=True, multiplicities=True` would already raise a
 `NotImplementedException` earlier on.
 * Not messing around with `repr(x) in …` is certainly a good thing.
 * The move from `Y = ….sage()` to `T =
 string_to_list_of_solutions(repr(s))` I don't understand yet. Need a
 closer look.
 * The rationale behind `ignore_exceptions` I don't understand either yet.

 A lot of this appears to be drive-by-fixes which make sense but are not
 immediately related to this bug here. Is that correct? Can you come up
 with doctests for the things these fix, if it's more than code
 simplification? For example I suppose that having one variable name as a
 substring of another might confuse this `repr(x)` hackery.

 I would prefer changing the `while todo: ex = todo.pop()` back to `for eq
 in todo:`. As it stands now, the idiom suggests that you might be adding
 stuff to the list within the loop. This even had me concerned about
 infinite loops for a moment. But you don't do that, you simply iterate
 over the list.

--
Ticket URL: <http://trac.sagemath.org/ticket/16651#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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