Run tests for `an_affine_basis`

[kliem]

This ticket adds a method that tests an_affine_basis to Polyhedron_base.

We move some basic tests there.

Depends on #29903

CC: @jplab @LaisRast

Component: geometry

Keywords: polyhedra, test suite

Author: Jonathan Kliem

Branch/Commit: f57e162

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29906

[sagetrac-git]

Changed commit from 5d79b2b to af2ba1f

[sagetrac-git]

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

af2ba1f

test suite for an_affine_basis

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

[sagetrac-git]

Changed commit from af2ba1f to 5d79b2b

[kliem]

Changed branch from public/29903 to public/29906

[kliem]

Dependencies: #29903

[kliem]

Changed commit from 5d79b2b to af2ba1f

[kliem]

New commits:

af2ba1f

test suite for an_affine_basis

[tscrim]

comment:4

Is there some way to improve this test:

m = matrix(b).transpose().stack(matrix([[1]*len(b)]))

It feels somewhat inefficient as you make a matrix then take its transpose. Plus you get a new matrix with the stack call. Wouldn't it be better to just add 1 to each of the vectors b then ask for the rank?

[kliem]

comment:5

It does feel inefficient, but I think it is rather efficient (besides that it really doesn't matter as obtaining an_affine_matrix takes much longer than anything else here):

sage: P = polytopes.permutahedron(7)

sage: 
sage: b = P.vertices()
sage: len(b)
5040
sage: P = polytopes.permutahedron(7)
sage: b = P.vertices()
sage: len(b)
5040
sage: def hom_matrix1(b):
....:     return matrix(b).transpose().stack(matrix([[1]*len(b)]))
....: 
sage: def hom_matrix2(b):
....:     return matrix([1] + list(x) for x in b)
....: 
sage: def hom_matrix3(b):
....:     return matrix(b).transpose().stack(vector([1]*len(b)))
....: 
....: 
sage: %timeit hom_matrix1(b)
10 loops, best of 5: 19.6 ms per loop
sage: %timeit hom_matrix2(b)
10 loops, best of 5: 23.4 ms per loop
sage: %timeit hom_matrix3(b)
10 loops, best of 5: 26 ms per loop

sage: b = P.an_affine_basis()
sage: len(b)
sage: %timeit hom_matrix1(b)
The slowest run took 98.27 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 5: 46.1 µs per loop
sage: %timeit hom_matrix2(b)
The slowest run took 12.89 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 5: 35.1 µs per loop
sage: %timeit hom_matrix3(b)
The slowest run took 4.52 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 5: 103 µs per loop

So it is a bit faster for small instances (which should always be true for b being an affine basis of any TestSuite polyhedron, but really not by much. Besides it is a meaningless time difference if you consider obtaining an_affine_basis first, even with #29841.

If you know argue that matrix([1] + list(x) for x in b) is much easier to understand, I agree with you and that is a good point.