#9188: lattice_polytope.facet_normal bug with polytopes of less that full
dimension
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   Reporter:  vbraun              |       Owner:  novoselt    
       Type:  defect              |      Status:  needs_review
   Priority:  major               |   Milestone:  sage-4.4.4  
  Component:  geometry            |    Keywords:              
     Author:  Volker Braun        |    Upstream:  N/A         
   Reviewer:  Andrey Novoseltsev  |      Merged:              
Work_issues:                      |  
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Comment(by novoselt):

 OK, my patch looks big, but the only real change to the original is taking
 the absolute value of the dual scaling factor, so that normals remain
 inner.

 In addition I (hopefully) made doctests more clear, since they do appear
 in the documentation. Polytopes are now created using coordinates of
 points with all the necessary transpositions after that. I also made
 doctest lines shorter for better looks of the documentation.

 I have changed "parallel" to "orthogonal to integer kernel" in the
 description of normals (and now I do remember that I didn't like this
 "parallel" when I wrote it...).

 If you are fine with all these changes, I will switch it to positive
 review. Thank you for catching this bug!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9188#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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