#8800: Doctest coverage of categories - numerous coercion fixes
--------------------------+-------------------------------------------------
   Reporter:  SimonKing   |       Owner:  Simon King         
       Type:  defect      |      Status:  needs_work         
   Priority:  major       |   Milestone:  sage-4.6.2         
  Component:  categories  |    Keywords:  categories doctests
     Author:  Simon King  |    Upstream:  N/A                
   Reviewer:              |      Merged:                     
Work_issues:              |  
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Changes (by lftabera):

  * status:  needs_review => needs_work


Comment:

 Hi Simon,

 I am reading the code, it is a long patch but looks good, thanks for the
 work done.

 I have a question about functor AlgebraicExtensionFunctor and ZZ.
 According to the documentation:

 When applying a number field constructor to the ring of integers, the
 maximal order in the number field is returned::

 Why is this chosen instead of ZZ[x]/polynomial?

 Actually, the code does not follow the documentation except for
 CyclotomicField:

 {{{
 sage: N = NumberField(x^2 - 5, 'a')
 sage: F, R = N.construction()
 sage: F(ZZ).gens()
 [1, a]
 sage: F(ZZ).is_maximal()
 False
 sage: N.maximal_order().gens()
 [1/2*a + 1/2, a]
 }}}

 I add a patch that contains some small improvements (in my opinion). A
 couple of small tests and some style. Plase consider merging some of these
 changes. For example, in the code you usually write:

 return

 instead of

 return None

 Both are correct but, unless there are other reasons I am unaware, the
 second looks more readable to me (just an opinion).

 I have not yet finish to review the whole patch, so you may consider
 waiting untill I am done. I have to compile the documentation and check
 that the list of bugs you have solved appears in the TESTS of the patch.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8800#comment:68>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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