#8543: EmptySet is Back ! TestSuite should allows for empty sets.
------------------------------+---------------------------------------------
   Reporter:  hivert          |       Owner:  hivert                            
 
       Type:  defect          |      Status:  needs_review                      
 
   Priority:  major           |   Milestone:  sage-4.4                          
 
  Component:  categories      |    Keywords:  empty set, Testsuite, 
EmptySetError
     Author:  Florent Hivert  |    Upstream:  N/A                               
 
   Reviewer:                  |      Merged:                                    
 
Work_issues:                  |  
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Changes (by hivert):

  * keywords:  empty set, Testsuite => empty set, Testsuite, EmptySetError
  * status:  new => needs_review


Old description:

> There is currently no way to have an empty set which pass the category
> tests. Indeed the current specification says: for any set {{{S}}} there
> must be a method {{{S.an_element()}}} which returns an actual element
> {{{x}}} such that {{{x in S}}}:
> {{{
> an_element = self.an_element()
> tester.assert_(an_element in self, "self.an_element() is not in self")
> }}}
> This tests should allows {{{S}}} to be empty.

New description:

 There is currently no way to have an empty set which pass the category
 tests. Indeed the current specification says: for any set {{{S}}} there
 must be a method {{{S.an_element()}}} which returns an actual element
 {{{x}}} such that {{{x in S}}}:
 {{{
 an_element = self.an_element()
 tester.assert_(an_element in self, "self.an_element() is not in self")
 }}}
 This tests should allows {{{S}}} to be empty.

 To solve this issue I added a new exception called {{{EmptySetError}}}
 which should be raised in such cases. I fixed the tests suite of the
 category {{{Sets()}}} accordingly and expanded the test in some places
 where this could be done before.

 Depends on #8519

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8543#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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