#8562: Categories for IntegerMod rings
-----------------------------------------------------------------+----------
   Reporter:  nthiery                                            |       Owner: 
 AlexGhitza                   
       Type:  defect                                             |      Status: 
 needs_work                   
   Priority:  major                                              |   Milestone: 
 sage-5.0                     
  Component:  algebra                                            |    Keywords: 
 categories, integer mod rings
     Author:  Nicolas M. ThiƩry                                  |    Upstream: 
 N/A                          
   Reviewer:  Robert Beezer                                      |      Merged: 
                              
Work_issues:  Designe decision for IntegerModRing(5).category()  |  
-----------------------------------------------------------------+----------
Changes (by nthiery):

  * status:  needs_review => needs_work
  * work_issues:  (didn't run full tests yet) => 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
> }}}
>
> This is required to use the cool features from #7555.

New 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

--

Comment:

 > David: I won't be touching this patch further. Feel free to update /
 refactor / merge /... it within the other series of patch whenever it
 feels right.

 Note: I meant David Roe, but any other David is welcome too :-)

 Oh: would you agree to take over that patch, and finalize it (or ping me)
 when it's ripe to get in?

 (then I could forget about it).

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8562#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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