#20330: hyperbolic_geodesic midpoint bugfix
-------------------------------------+-------------------------------------
       Reporter:  jhonrubia6         |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.2
      Component:  geometry           |   Resolution:
       Keywords:  hyperbolic         |    Merged in:
  geometry, geodesic                 |    Reviewers:  Vincent Delecroix
        Authors:  Javier Honrubia    |  Work issues:
  González                           |       Commit:
Report Upstream:  N/A                |  2ba1c96e25d7e128adc832bc4c4e4c51e8835b98
         Branch:                     |     Stopgaps:
  u/jhonrubia6/hyperbolic_geodesic_midpoint_bugfix|
   Dependencies:                     |
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Comment (by nbruin):

 Replying to [comment:46 jhonrubia6]:

 > I am out of my field here, but if I understand you right, are you
 proposing to replace the elif block proposed by Vincent by something based
 on the CyclotomicField? Why is it more robust? aside of the problems you
 mention of {{{CC(CyclotomicField(4).0)}}} which may be should be
 accomplished on a different ticket

 There is no particular reason for P.gen(0) to be a fourth root of unity,
 even if P contains a fourth root of unity. Therefore, the proposed code
 can easily fail if it doesn't really have to. Hence, it would be nice to
 express intent a little more explicitly here. For `CyclotomicField(4)`
 it's clear its generator is a fourth root of unity, so that's a candidate
 for a "universal" place to find such an element. I'm not so sure it's the
 best place, but it's at least a place to hook into the general conversion
 infrastructure.

--
Ticket URL: <http://trac.sagemath.org/ticket/20330#comment:48>
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