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

 Replying to [comment:40 SimonKing]:
 > A while ago, I had worked on a ticket #10667 about category containment.
 One purpose was to get a speedup. The trick was (again) to use Cython. For
 some reason, the work on that ticket has stalled. Perhaps it would be
 worth while to resume it.
 >

 +1

 > Generally, I think it is better to improve the category framework,
 rather than to work around it.
 >
 > >  For example, see #11657, where one of the root causes of slowness was
 code in is_Ring that was added to support this category approach, and
 which slowed everything down.
 >
 > Then why is the existing `is_Ring` not rewritten along the lines of what
 you do in #11657?

 What I did there slows down {{{is_Ring}}} testing if the object in
 question does not derive from Ring.

 > > is_Ring is only deprecated when used from the top level (i.e., the
 Sage prompt).
 >
 > Yes, this is what I meant. I did not mean "deprecated" in the sense of
 "will soon be removed", but in the sense of "please don't try this at
 home".
 >

 If you are developing on the Sage library, I think it is OK to use.

 > >  And the is_Ring function does test for category stuff.
 >
 > Actually I have not been aware that category stuff is tested in
 `is_Ring`. I was thinking about various other `is_...` methods that really
 do nothing more than isinstance.
 >

 Yes, take a look at the code.  I too was surprised by this!

  -- William

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9054#comment:41>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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