Set up linear transformation with precomputed data if injective #29843
Description
We set up linear transformation with double description, if it preserves the polytope.
Also we slightly modify the affine hull projection to make use of this.
Before this ticket:
(Run tests twice to obtain the real timinigs. The first time it computes twice to populate the coercion model, see https://groups.google.com/d/msg/sage-devel/UAvbXKSN_JU/vcVN2AVQBQAJ)
sage: P = polytopes.permutahedron(6)
sage: %time Q = P.affine_hull_projection()
CPU times: user 94.1 ms, sys: 2 µs, total: 94.1 ms
Wall time: 93.5 ms
sage: P = polytopes.permutahedron(7)
sage: %time Q = P.affine_hull_projection()
CPU times: user 2.21 s, sys: 1 µs, total: 2.21 s
Wall time: 2.21 s
sage: P = polytopes.permutahedron(4)
sage: %time Q = P.affine_hull_projection(orthonormal=True, extend=True)
CPU times: user 1.36 s, sys: 2 µs, total: 1.36 s
Wall time: 1.36 s
sage: P = polytopes.hypercube(13)*Polyhedron(vertices=[[0]])
sage: %time Q = P.affine_hull_projection()
CPU times: user 1.84 s, sys: 5 µs, total: 1.84 s
Wall time: 1.84 s
With this ticket on top of #29841 (this tickets new implementation uses CombinatorialPolyhedron which is much faster obtained with #29841):
sage: P = polytopes.permutahedron(6)
sage: %time Q = P.affine_hull_projection()
CPU times: user 78.9 ms, sys: 0 ns, total: 78.9 ms
Wall time: 77.7 ms
sage: P = polytopes.permutahedron(7)
sage: %time Q = P.affine_hull_projection()
CPU times: user 1.23 s, sys: 35 µs, total: 1.23 s
Wall time: 1.23 s
sage: P = polytopes.permutahedron(7)
sage: P = P.base_extend(P.base_ring(), backend='field')
sage: %time Q = P.affine_hull_projection()
CPU times: user 366 ms, sys: 3.98 ms, total: 370 ms
Wall time: 369 ms
sage: P = polytopes.permutahedron(4)
sage: %time Q = P.affine_hull_projection(orthonormal=True, extend=True)
CPU times: user 187 ms, sys: 10.8 ms, total: 198 ms
Wall time: 196 ms
sage: P = polytopes.hypercube(13)*Polyhedron(vertices=[[0]])
sage: %time Q = P.affine_hull_projection()
CPU times: user 847 ms, sys: 36 µs, total: 848 ms
Wall time: 846 ms
Component: geometry
Author: Jonathan Kliem
Branch/Commit: 28819ea
Reviewer: Matthias Koeppe
Issue created by migration from https://trac.sagemath.org/ticket/29843