affine_basis does not always work when used with orthogonal or orthonormal

[LaisRast]

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

CC: @jplab @kliem

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

[kliem]

Dependencies: #29127

[kliem]

New commits:

a8359e0	implement `a_maximal_chain` for combinatorial polyhedron
6c4c1c0	implement `an_affine_basis` for polytopes
3d87ccf	more description in the docs
1b78e87	used an_affine_basis to simplify is_inscribed
5e547b3	check sign of circumcenter using all vertices of simplex
231c16f	apply change to 29125
4fb0f6b	handling small-dimensional cases
3f6013b	temporary fix
df7ec00	get correct affine basis for affine hull with orthogonal/orthonormal

[kliem]

Author: Jonathan Kliem

[kliem]

Commit: df7ec00

[kliem]

Branch: public/29116

[kliem]

Changed commit from df7ec00 to 8b2709e

[kliem]

Changed branch from public/29116 to public/29116-reb

[kliem]

New commits:

61dd4a5	implement `a_maximal_chain` for combinatorial polyhedron
a18011f	improved documentation
2e9f25f	exposed a_maximal_chain to polyhedron_base
0315652	implement `an_affine_basis` for polytopes
554556d	more description in the docs
aa30035	used an_affine_basis to simplify is_inscribed
08b263e	apply change to 29125
d2d2a8a	handling small-dimensional cases
ba48b17	get correct affine basis for affine hull with orthogonal/orthonormal
8b2709e	temporary fix

[LaisRast]

comment:4

Since #29127 is on "positive review", I think this one also should be on "positive review".
It looks good to me.
(pycodestyle warnings are not sourced from her)

[LaisRast]

Reviewer: Laith Rastanawi

[LaisRast]

comment:5

I forgot to mention:

-            # We implicitely translate the first vertex of the affine basis to zero.
+            # We implicitly translate the first vertex of the affine basis to zero.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

7d21717

typo

[sagetrac-git]

Changed commit from 8b2709e to 7d21717

[vbraun]

Changed branch from public/29116-reb to 7d21717