Dear developers,

I have just posted a series of patches implementing toric varieties in
Sage and will be very grateful if someone (or maybe even somemany!)
could help reviewing them. There are 3 patches in algebraic geometry
slightly modifying schemes modules, 3 small patches for lattice
polytopes (2 are already reviewed!), and 4 patches adding one module
each, so that the new additions are easier to review. Here they are:

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 (positively reviewed by Volker Braun)
#8936 - Expose facet inequalities for lattice polytopes
#8941 - _latex_ and origin for lattice polytopes (positively reviewed
by Volker Braun)

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.

Potential reviewers may want to check /scratch/novoselt/sage-4.4.2.rc0-
toric on sage.math, which contains a fresh installation of Sage with
the above 10 patches applied. (I didn't do anything with access
rights, so I hope that anyone who has an account can use it.)

Also, compiled documentation is available at
http://sage.math.washington.edu/home/novoselt/en/reference/sage/geometry/cone.html
http://sage.math.washington.edu/home/novoselt/en/reference/sage/geometry/fan.html
http://sage.math.washington.edu/home/novoselt/en/reference/sage/schemes/generic/toric_variety.html
http://sage.math.washington.edu/home/novoselt/en/reference/sage/schemes/generic/fano_toric_variety.html

Hopefully, these patches can be merged soon, as while I was working on
these modules Volker Braun also was working on toric varieties, see
http://groups.google.com/group/sage-devel/browse_thread/thread/4100e7ced408f1e2#
The natural question is: should we merge his patches or mine? While I
am obviously biased, I think that we should first merge mine, which
provide basic framework, and then merge Volker's on top of mine with
necessary changes, since he was working more in the "mathematical"
direction rather than "frameworking."

Thank you!
Andrey

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