#8986: Add support for convex rational polyhedral cones
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   Reporter:  novoselt            |       Owner:  mhampton    
       Type:  enhancement         |      Status:  needs_review
   Priority:  major               |   Milestone:  sage-4.4.2  
  Component:  geometry            |    Keywords:              
     Author:  Andrey Novoseltsev  |    Upstream:  N/A         
   Reviewer:                      |      Merged:              
Work_issues:                      |  
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Changes (by newvalueoldvalue):

  * status:  new => needs_review
  * milestone:  => sage-4.4.2
  * author:  => Andrey Novoseltsev


Old description:



New description:

 This patch is a part of the following series adding support for cones/fans
 and toric varieties to Sage:

 Prerequisites:

 #8675 - Remove {{{AmbientSpace._constructor}}} and fix consequences

 #8682 - Improve {{{AlgebraicScheme_subscheme.__init__}}} and
 {{{AmbientSpace._validate}}}

 #8694 - Improve schemes printing and !LaTeXing

 #8934 - Trivial bug in computing faces of non-full-dimensional lattice
 polytopes

 #8936 - Expose facet inequalities for lattice polytopes

 #8941 - {{{_latex_}}} and {{{origin}}} for lattice polytopes

 Main patches adding new modules:

 #8986 - Add support for convex rational polyhedral cones

 #8987 - Add support for rational polyhedral fans

 #8988 - Add support for toric varieties

 #8989 - Add support for Fano toric varieties

 Everything was tested on sage.math using sage-4.4.2.rc0.

 Known issues:

 - Applying patch for toric varieties leads to a doctest error in
 {{{sage.symbolic.random_tests}}}, which I don't quite understand,
 especially since this patch just adds a new module! The documentation of
 the failing function says "This function will often raise an error because
 it tries to create an erroneous expression." I am not sure if this means
 that its doctest may cause these errors.

 - The last two patches show a doctest coverage error about
 {{{TestSuite}}}. This doctest does not work yet for other schemes and
 therefore should not be expected to work for these derived classes (and
 indeed - it does not work). According to
 http://groups.google.com/group/sage-
 devel/browse_thread/thread/a42ace80078373b4
 this should not be an obstacle to include these patches.

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8986#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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