Set up permutahedron with both Vrep and Hrep (if backend supports it)

[kliem]

We set up the permutahedron with both Vrepresenation and Hrepresentation, if the backend supports it.

If the backend supports precomputed data (currently field) this is much faster. Otherwise, this is a bit faster, as the Hrepresentation seems to be the better choice.

Before this ticket:

sage: %timeit P = polytopes.permutahedron(6)  # using ppl
10 loops, best of 5: 56.5 ms per loop
sage: %timeit P = polytopes.permutahedron(7)  # using ppl
1 loop, best of 5: 1.57 s per loop

With this ticket:

sage: %timeit P = polytopes.permutahedron(6)  # using ppl
10 loops, best of 5: 34.2 ms per loop
sage: %timeit P = polytopes.permutahedron(7)  # using ppl
1 loop, best of 5: 1.04 s per loop
sage: %time P = polytopes.permutahedron(8, backend='field')
CPU times: user 587 ms, sys: 20 ms, total: 607 ms
Wall time: 607 ms
sage: %time P = polytopes.permutahedron(9, backend='field')
CPU times: user 5.08 s, sys: 248 ms, total: 5.33 s
Wall time: 5.33 s

Note that field is much slower than ppl before this ticket and the timings are therefore omitted.

As the order of Vrepresentation and Hrepresentation changes, a lot of tests need to be fixed.

CC: @jplab @LaisRast

Component: geometry

Keywords: polytopes, precomputed data, permutahedron

Author: Jonathan Kliem

Branch/Commit: 577e736

Reviewer: Jean-Philippe Labbé, Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/29325

[kliem]

New commits:

33e4490	set up permutahedron with precomputed data
32708d4	fixing failing doctests due to reordering

[kliem]

Commit: 32708d4

[kliem]

Branch: public/29325

[mkoeppe]

comment:2

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[kliem]

Changed commit from 32708d4 to 3174e62

[kliem]

New commits:

24f2a4a	set up permutahedron with precomputed data
3174e62	fixing failing doctests due to reordering

[kliem]

Changed branch from public/29325 to public/29325-reb2

[jplab]

Reviewer: Jean-Philippe Labbé

[jplab]

comment:4

These timings are interesting. Perhaps it would be good to add them to the documentation of the function? Since the backend field performs well but isn't the default, it would be good to give this information in the documentation.