#20330: hyperbolic_geodesic midpoint bugfix
-------------------------------------+-------------------------------------
       Reporter:  jhonrubia6         |        Owner:
           Type:  defect             |       Status:  needs_work
       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 jhonrubia6):

 I've also modified the doctoring in {{{_to_std_geod()}}} method since it
 randomly failed (depending on the random UHP points, for example:
 {{{
 sage: UHP = HyperbolicPlane().UHP()
 sage: p1=0.869685163129173 + 0.897487924526729*I
 sage: p2=5.71917016919078 + 7.09666543326670*I
 sage: g = UHP.get_geodesic(p1, p2)
 sage: p= g.midpoint().coordinates()
 sage: A = g._to_std_geod(p);A # Send midpoint to I.
 sage: A = UHP.get_isometry(A)
 sage: [s, e]= g.complete().endpoints();s;e;p
 sage: bool(abs(A(s).coordinates()) < 10**-9)
 True
 sage: bool(abs(A(g.midpoint()).coordinates() - I) < 10**-9)
 True
 sage: bool(A(e).coordinates() == infinity)
 False
 sage: bool(abs(A(e).coordinates())>10**9)
 True
 }}}

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Ticket URL: <http://trac.sagemath.org/ticket/20330#comment:23>
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