#8987: Add support for rational polyhedral fans
----------------------------------+-----------------------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.4.4
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Old 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:
>
> #9062 - Add support for toric lattices
>
> #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.
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:
#9062 - Add support for toric lattices
#8986 - Add support for convex rational polyhedral cones
#8987 - Add support for rational polyhedral fans (this ticket now also has
a bug fix #9188 as a prerequisite)
#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.
--
Comment(by novoselt):
I posted a preliminary version towards addressing all the issues. So far I
worked only on face order and a doctest for #9188.
For fans the last level of the cone_lattice is now inaccessible through
`cones()` method, because it is a fan and not a cone.
If the generating cones are of different dimensions, no attempt is made to
sort the corresponding faces in any way since "perfect matching" is not
possible anyway.
Middle dimensional faces are never sorted - it is not difficult to sort
them, say, by generating rays, but I am not sure what can be a benefit of
this. Let me know if you have a different opinion on this.
P.S. Sorting is sort of done twice - once is the Hasse diagram function
and then in face_lattice/cone_lattice. The reason is that I thought that
the first one will be enough and then didn't want to remove it since it
seems to be nice too.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8987#comment:19>
Sage <http://www.sagemath.org>
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