#20301: Polyhedron.to_linear_program should return the MIP variable used
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   Reporter:  mkoeppe   |            Owner:
       Type:  defect    |           Status:  new
   Priority:  major     |        Milestone:  sage-7.2
  Component:  geometry  |         Keywords:
  Merged in:            |          Authors:
  Reviewers:            |  Report Upstream:  N/A
Work issues:            |           Branch:
     Commit:            |     Dependencies:
   Stopgaps:            |
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 #18815 introduced `Polyhedron.to_linear_program` -- but there's very
 little one can do with it.
 To
  - set an objective other than the default 0;
  - access an optimal solution vector after solving,
 one needs the MIP variable (`x` in the code of `to_linear_program`).
 Currently the only way to do anything is by using the MIP backend.

 I would propose to return `x` as a second return value, but this of course
 changes the interface.

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Ticket URL: <http://trac.sagemath.org/ticket/20301>
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