Subdivide fans using PPL

[novoselt]

Current Fan.subdivide() method cannot deal with fans generated by non-full-dimensional cones since it relies on PALP. In addition it is overly complicated. So let's use PPL cones for subdivision, since our toric cones already rely on them a lot. Speed-wise new method seems to work 2-3 times faster than the old one, but main advantages are brevity of code and absence of artificial limitations.

I've also cleaned up related code a bit and deprecated Cone.lattice_polytope whose primary purpose was to use PALP for subdivision.

CC: @vbraun @sagetrac-jkeitel

Component: geometry

Keywords: toric

Author: Andrey Novoseltsev

Branch/Commit: 59c8c94

Reviewer: Jan Keitel

Issue created by migration from https://trac.sagemath.org/ticket/16180

[novoselt]

Branch: u/novoselt/subdivide_fans_using_ppl

[novoselt]

Commit: dc35d9d

[novoselt]

Author: Andrey Novoseltsev

[novoselt]

Description changed:

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+++ 
@@ -1 +1,3 @@
+Current `Fan.subdivide()` method cannot deal with fans generated by non-full-dimensional cones since it relies on PALP. In addition it is overly complicated. So let's use PPL cones for subdivision, since our toric cones already rely on them a lot. Speed-wise new method seems to work 2-3 times faster than the old one, but main advantages are brevity of code and absence of artificial limitations.
 
+I've also cleaned up related code a bit and deprecated `Cone.lattice_polytope` whose primary purpose was to use PALP for subdivision.

[novoselt]

New commits:

a692959	Use PPL for fan subdivision.
17cb30b	Fix doctests due to different facet ordering in PPL and PALP.
dc35d9d	Deprecate Cone.lattice_polytope() and drop cache for Cone.polyhedron().

[novoselt]

Changed keywords from none to toric

[sagetrac-jkeitel]

comment:5

Hi Andrey,

I've looked at the patch at it looks good - it's always nice to get rid of LatticePolytope. ;-)
One quick question: Is there any reason you're not caching the polyhedron() method of Cone?

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New commits:

bd66bcd	Merge branch 'develop' into u/novoselt/subdivide_fans_using_ppl
f7f0dd5	Ticket 16180: Two minor formatting changes.

[sagetrac-jkeitel]

Changed commit from dc35d9d to f7f0dd5