#12967: bugs in comparisons between constants, wrapped pyobjects, infinity
-------------------------------------+-------------------------------------
       Reporter:  dkrenn             |        Owner:  burcin
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.6
      Component:  symbolics          |   Resolution:
       Keywords:  compare pi         |    Merged in:
  infinity bool                      |    Reviewers:  Karl-Dieter Crisman
        Authors:  Travis Scrimshaw,  |  Work issues:
  Ralf Stephan                       |       Commit:
Report Upstream:  N/A                |  c5845f6b18d582807dafaaf60ad6a5c8017173f3
         Branch:  u/rws/12967-2      |     Stopgaps:
   Dependencies:  #17984             |
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Changes (by pbruin):

 * status:  needs_review => needs_work


Comment:

 I'm afraid this implementation of `__contains__()` will make `Mod(1, 2) in
 RR` return `True`, which is obviously wrong.  This is probably the reason
 why the nonsense input in the Chebyshev doctests is no longer detected.

 I am in general hesitant about the idea of needing a custom
 `__contains__()` method; the strategy to implement `x in P` as `bool(P(x)
 == x)` basically seems a good one to me.  How about fixing `__cmp__()` (or
 similar) when comparing symbolic expressions with numerical approximations
 so that (for example)  `bool(pi == 3.14[...])` returns `True` if the
 approximation is correct to the given precision?

--
Ticket URL: <http://trac.sagemath.org/ticket/12967#comment:35>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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