#8562: Categories for IntegerMod rings
---------------------------------+------------------------------------------
   Reporter:  nthiery            |       Owner:  AlexGhitza                   
       Type:  enhancement        |      Status:  needs_review                 
   Priority:  major              |   Milestone:  sage-4.4                     
  Component:  algebra            |    Keywords:  categories, integer mod rings
     Author:  Nicolas M. ThiƩry  |    Upstream:  N/A                          
   Reviewer:                     |      Merged:                               
Work_issues:                     |  
---------------------------------+------------------------------------------
Changes (by nthiery):

  * status:  needs_work => needs_review
  * reviewer:  Robert Beezer =>
  * type:  defect => enhancement
  * work_issues:  Designe decision for IntegerModRing(5).category() =>


Old description:

> After this patch, IntegerModRing's inherit properly from categories:
> {{{
>     sage: Z3 = IntegerModRing(3)
>     sage: Z3.category()
>     Category of fields
>     sage: TestSuite(Z3).run(verbose = True)
>     running ._test_additive_associativity() . . . pass
>     running ._test_an_element() . . . pass
>     running ._test_associativity() . . . pass
>     running ._test_category() . . . pass
>     running ._test_elements() . . .
>       Running the test suite of self.an_element()
>       running ._test_category() . . . pass
>       running ._test_not_implemented_methods() . . . pass
>       running ._test_pickling() . . . pass
>       pass
>     running ._test_not_implemented_methods() . . . pass
>     running ._test_one() . . . pass
>     running ._test_pickling() . . . pass
>     running ._test_prod() . . . pass
>     running ._test_some_elements() . . . pass
>     running ._test_zero() . . . pass
> }}}
>
> And this makes the cool features from #7555 work for Z/nZ.
>
> Needs work: see: running design discussion on:
>
> http://groups.google.com/group/sage-devel/t/21e21e1ec9cd21fe

New description:

 After this patch, IntegerModRing's inherit properly from categories:
 {{{
     sage: Z3 = IntegerModRing(3)
     sage: Z3.category()
     Category of commutative rings
     sage: TestSuite(Z3).run(verbose = True)
     running ._test_additive_associativity() . . . pass
     running ._test_an_element() . . . pass
     running ._test_associativity() . . . pass
     running ._test_category() . . . pass
     running ._test_elements() . . .
       Running the test suite of self.an_element()
       running ._test_category() . . . pass
       running ._test_not_implemented_methods() . . . pass
       running ._test_pickling() . . . pass
       pass
     running ._test_not_implemented_methods() . . . pass
     running ._test_one() . . . pass
     running ._test_pickling() . . . pass
     running ._test_prod() . . . pass
     running ._test_some_elements() . . . pass
     running ._test_zero() . . . pass
 }}}

 And this makes the cool features from #7555 work for Z/nZ.

 Potential conflict with #8218 (which has higher priority)

 For a later ticket, see: running design discussion on:

 http://groups.google.com/group/sage-devel/t/21e21e1ec9cd21fe

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8562#comment:7>
Sage <http://www.sagemath.org>
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