#13814: LazyFamily.__eq__ gives false positives.
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   Reporter:  cnassau        |             Owner:  sage-combinat   
       Type:  defect         |            Status:  new             
   Priority:  major          |         Milestone:  sage-5.6        
  Component:  combinatorics  |          Keywords:                  
Work issues:                 |   Report Upstream:  N/A             
  Reviewers:                 |           Authors:  Christian Nassau
  Merged in:                 |      Dependencies:                  
   Stopgaps:                 |  
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 `LazyFamily.__eq__` occasionally returns false positives, because it only
 compares function names, not values. This can lead to subtle bugs later,
 like this one:

 {{{
 #!python
 fun = lambda i:i
 fam1 = LazyFamily((0,1),fun)
 fun = lambda i:i+6
 fam2 = LazyFamily((0,1),fun)
 fam3 = LazyFamily((2,3),fun)
 d1 = DisjointUnionEnumeratedSets((fam1,fam3))
 d2 = DisjointUnionEnumeratedSets((fam2,fam3))
 for u in (fam1,fam2,fam3,d1,d2):
     print list(u)
 }}}

 This gives

 {{{
 [0, 1]
 [6, 7]
 [8, 9]
 [0, 1, 8, 9]
 [0, 1, 8, 9]
 }}}

 because Sage thinks `fam1 == fam2`. The behaviour can be fixed by setting

 {{{
 def noteq(self,other):
     return False
 LazyFamily.__eq__ = noteq
 }}}

 I think `__eq__` should *never* give false positives for classes that
 might be hashed. In this case `LazyFamily.__eq__` should

    * test function equality if the index sets are finite of the same size
    * return `False` if the both index sets are infinite

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13814>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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