#15547: Dimension of a projection of a polyhedron
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   Reporter:  jipilab   |            Owner:
       Type:  defect    |           Status:  new
   Priority:  minor     |        Milestone:  sage-6.0
  Component:  geometry  |         Keywords:  tikz, projection
  Merged in:            |          Authors:  jipilab
  Reviewers:            |  Report Upstream:  N/A
Work issues:            |           Branch:
     Commit:            |     Dependencies:
   Stopgaps:            |
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 Using the new tikz feature, (see http://trac.sagemath.org/ticket/12083)
 there is a problem when drawing polygons embedded in 3d. The error can be
 reproduced:

 {{{
     sage: P = Polyhedron(vertices=[[1,0,0],[0,1,0],[0,0,1]])
     sage: P.ambient_dim()
     3
     sage: P.dim()
     2
     sage: PProj = P.projection()
     sage: PProj.polyhedron_ambient_dim
     3
     sage: PProj.dimension
     3
 }}}

 I believe PProj.dimension should be 2, not 3. Because of this, the tikz
 method misbehaves.

 In this case, the function _init_from_3d(self, polyhedron) used for
 projection contains:

 {{{
     assert polyhedron.ambient_dim() == 3, "Requires polyhedron in 3d"
     self.dimension = 3
     self._init_points(polyhedron)
 }}}

 I believe one should replace the second line by

 {{{
     self.dimension = polyhedron.dim()
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/15547>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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