Use PPL for computing vertices of LatticePolytope

[novoselt]

This gives drastic improvement for small polytopes which is the target case. Before:

sage: timeit("LatticePolytope(lattice_polytope.cross_polytope(3).vertices())")
25 loops, best of 3: 35.2 ms per loop

After:

sage: timeit("LatticePolytope(lattice_polytope.cross_polytope(3).vertices())")
625 loops, best of 3: 684 µs per loop

Next in the chain of lattice polytope improvements is #22310

Depends on #22304

CC: @vbraun

Component: geometry

Author: Andrey Novoseltsev

Branch/Commit: c820307

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/22309

[novoselt]

Branch: u/novoselt/PPL_for_vertices

[novoselt]

Commit: db3b54e

[novoselt]

comment:2

Volker, I was going to stop bugging you, but this great speed up is mostly due to what you've done for cones, I've just adjusted it to work with points rather than rays.

---

New commits:

a262ec3	Make dual nef-partitions conveniently ordered
6b5972c	Fix nef-partition ordering in doctests
2e26768	Add NefCompleteIntersection.cohomology_class
7afca73	Add Cayley polytopes/cones to dosctring of NefPartition
e78ff49	Add PPL representation to LatticePolytope
5c286e4	Use PPL for computing vertices of LatticePolytope
db3b54e	Fix doctests - mostly due to different order of vertices

[novoselt]

Description changed:

--- 
+++ 
@@ -10,3 +10,4 @@
 sage: timeit("LatticePolytope(lattice_polytope.cross_polytope(3).vertices())")
 625 loops, best of 3: 684 µs per loop
 ```
+Next in the chain of lattice polytope improvements is #22310

[tscrim]

comment:4

For multiline imports, you can use (IMO cleaner):

from sage.libs.ppl import (C_Polyhedron, Generator_System, Linear_Expression,
                           point as PPL_point)

Otherwise LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[sagetrac-git]

Changed commit from db3b54e to c820307

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c820307

Use parentheses for multiline import

[novoselt]

comment:7

Thank you! I've checked with PEP 8 that this is also the recommended way of doing things - will try to keep in mind for the future. So - positive review?-)

[tscrim]

comment:8

Yes indeed.