#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                |  663a76cb67fb1598301ce842dccd8341ab07218b
         Branch:                     |     Stopgaps:
  u/jhonrubia6/hyperbolic_geodesic_midpoint_bugfix|
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by vdelecroix):

 You might want to add some doctest similar to the following to check that
 floating points remain floating points in any method.
 {{{
 sage: g = UHP.get_geodesic(CC(0,1), CC(2,2))
 sage: UHP.dist(g.start(), g.end())
 1.45057451382258
 sage: parent(_)
 Real Field with 53 bits of precision
 sage: g.midpoint()
 Point in UHP 0.666666666666666 + 1.69967317119759*I
 sage: parent(g.midpoint().coordinates())
 Complex Field with 53 bits of precision
 sage: gc = g.complete()
 Geodesic in UHP from -0.265564437074637 to 3.76556443707464
 sage: parent(gc.start().coordinates())
 Real Field with 53 bits of precision
 sage: parent(gc._to_std_geod(g.start().coordinates()))
 Full MatrixSpace of 2 by 2 dense matrices over Complex Field with 53 bits
 of precision
 }}}

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Ticket URL: <http://trac.sagemath.org/ticket/20330#comment:26>
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