affine_basis does not always work when used with orthogonal or orthonormal #29116
Description
When using affine_basis of Polyhedron with orthogonal or orthonormal we get the following errors.
sage: V =[
....: [1, 0, -1, 0, 0],
....: [1, 0, 0, -1, 0],
....: [1, 0, 0, 0, -1],
....: [1, 0, 0, +1, 0],
....: [1, 0, 0, 0, +1],
....: [1, +1, 0, 0, 0]
....: ]
sage: P = Polyhedron(V)
sage: P.affine_hull()
A 4-dimensional polyhedron in ZZ^4 defined as the convex hull of 6 vertices
sage: P.affine_hull(orthogonal=True)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
...
ValueError: V-representation data requires a list of length ambient_dim
sage: P.affine_hull(orthonormal=True, extend=True)
A 4-dimensional polyhedron in AA^4 defined as the convex hull of 5 vertices and 1 line
This happens because the method for computing an affine basis depends on the order of the vertices. We fix that by computing an affine basis of the polyhedron in the right way.
Depends on #29127
Component: geometry
Keywords: polytopes, affine_hull
Author: Jonathan Kliem
Branch/Commit: 7d21717
Reviewer: Laith Rastanawi
Issue created by migration from https://trac.sagemath.org/ticket/29116