#8327: Implement the universal cyclotomic field, using Zumbroich basis
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       Reporter:  nthiery                            |         Owner:           
   
           Type:  enhancement                        |        Status:  
needs_review
       Priority:  major                              |     Milestone:  sage-5.6 
   
      Component:  number fields                      |    Resolution:           
   
       Keywords:  Cyclotomic field, Zumbroich basis  |   Work issues:           
   
Report Upstream:  N/A                                |     Reviewers:           
   
        Authors:  Christian Stump, Simon King        |     Merged in:           
   
   Dependencies:  #13727, #13728                     |      Stopgaps:           
   
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Comment (by nthiery):

 Replying to [comment:144 chapoton]:
 > I suspect (without a really good reason) that the choice of the letter
 E, which is a traditional name for elliptic curves, may be involved..

 Possibly, if E occurs explicitly in the doctest. Otherwise it should not
 interfer, as it is only imported by default in the intepreter and not in
 the sage sources. An alternative possibility is that some coercion
 involving cyclotomic fields now goes through UCF and causes trouble. You
 could rerun the failing tests with all the UCF coercions disabled.

 > By the way, is it reasonable to use a single letter ? I myself do not
 like the fact that the letter R stands for something I do not care about..
 Maybe one could ask the question on sage-devel : can we use the name E for
 the generators of the universal cyclotomic field ?

 That's a good point. The average Sage user is indeed different from the
 average GAP user. An alternative would be to use UCF.E, and to implement:
 {{{
     sage: UCF.inject_shorthands()
     sage: E(3)
 }}}
 (as for symmetric functions)

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8327#comment:145>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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