gale_transform does not work for RDF

[kliem]

Currently the Gale transform for RDF does not work

sage: P = polytopes.icosahedron(exact=False)
sage: sum(P.gale_transform())
(1.3819660112000005, -1.3819660112000005, 0.3819660112000003, -1.3819660112000005, -9.43689570931383e-16, 1.6653345369377348e-16, -6.661338147750939e-16, 0.0)

but the sum should be close to zero. This is of course only an indication that something goes terribly wrong. For #29065, I wanted to add a doctest recovering an inexact polyhedron from the gale diagram, but it simply does not work.

The problem is quite simple. The method right_kernel for matrices, should just not be used, as it echolonizes the kernel. This is just something, one shouldn't do for inexact rings. The method right_kernel_matrix(basis=computed) gives a much more useful matrix.

We also leave a note in left_kernel, right_kernel, and right_kernel_matrix to indicate this problem.

CC: @jplab @LaisRast

Component: geometry

Keywords: polytopes, gale transform, RDF

Author: Jonathan Kliem

Branch/Commit: 9683151

Reviewer: Laith Rastanawi

Issue created by migration from https://trac.sagemath.org/ticket/29073

[kliem]

Branch: public/29073

[kliem]

Commit: 29f9ebe

[kliem]

New commits:

1db3349	add notes about not echolonizing kernels for inexact rings
29f9ebe	do not echolonize kernel basis for gale transpose

[kliem]

Author: Jonathan Kliem

[sagetrac-git]

Changed commit from 29f9ebe to cfd9b1a

[sagetrac-git]

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

cfd9b1a

fixed doc indent

[LaisRast]

comment:3

In left_kernel, explain your note a little bit:

             For inexact rings use :meth:`right_kernel_matrix` with
-            ``basis='computed'`` to avoid echolonizing.
+            ``basis='computed'`` (on the transpose of the matrix) to avoid echolonizing.

Otherwise, it is good to go.

[sagetrac-git]

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

9683151

better comment in doc of left_kernel

[sagetrac-git]

Changed commit from cfd9b1a to 9683151

[LaisRast]

Reviewer: Laith Rastanawi

[vbraun]

Changed branch from public/29073 to 9683151