#9054: create a class for basic function_field arithmetic for Sage
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    Reporter:  was                                                              
               |         Owner:  was                          
        Type:  enhancement                                                      
               |        Status:  needs_review                 
    Priority:  major                                                            
               |     Milestone:  sage-4.7.2                   
   Component:  algebra                                                          
               |    Resolution:                               
    Keywords:                                                                   
               |   Work_issues:                               
    Upstream:  N/A                                                              
               |      Reviewer:  Maarten Derickx, Julian Rueth
      Author:  William Stein, Robert Bradshaw, Maarten Derickx, Moritz 
Minzlaff, Julian Rueth  |        Merged:                               
Dependencies:  #9094, #11751, #9138                                             
               |  
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Comment(by saraedum):

 (Apparently the patchbot expects these "Apply" instructions in a comment
 and not in the ticket description)

 A more detailed description of the patches since
 {{{trac_9054-invert_ideal.patch}}}:

  * {{{trac_9054_isFunctionField.patch}}} hopefully does what Simon King
 proposed for {{{is_FunctionField}}}
  * {{{trac_9054_UniqueFactory.patch}}} replaces the {{{@cached_method}}}
 in {{{constructor.py}}} with UniqueFactories -- apparently that class is
 meant for that purpose
  * {{{trac_9054_cached_method.patch}}} replaces all manual caching with
 {{{@cached_method}}} methods
  * {{{trac_9054_maximal_order_member_check.patch}}} fixes a todo about
 checking that members  passed to an {{{_element_constructor}}} are
 actually in the order
  * {{{trac_9054_call_super_constructors.patch}}} is the one I'm not sure
 about. At two places the super classes were not properly called -- was
 that by intention? I hope this fixes it.
  * {{{trac_9054_maps_refactor.patch}}} slightly changes the base classes
 of function field morphisms
  * {{{trac_9054_doctests-3.patch}}} essentially unifies the naming of
 variables in the doctests, so function fields are now called K and L,
 variables x, y, z. Also I added an entry to
 {{{/doc/en/reference/index.rst}}}, is that correct?
  * {{{trac_9054_cleanup.patch}}} reorganizes some imports and removes
 empty lines
  * {{{trac_9054_authors.patch}}} adds authors and copyrights to the files.
 I followed [http://www.sagemath.org/doc/developer/conventions.html
 #headings-of-sage-library-code-files], hopefully I got it right?

 I also reviewed Maarten's changes and they looked good except for the very
 few things I patched here. Maarten could you review my patches? It looks
 like a lot of work, but it should be fairly trivial to review.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9054#comment:56>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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