#29073 closed defect (fixed)

`gale_transform` does not work for `RDF`

Reported by: gh-kliem Owned by:
Priority: major Milestone: sage-9.1
Component: geometry Keywords: polytopes, gale transform, RDF
Cc: jipilab, gh-LaisRast Merged in:
Authors: Jonathan Kliem Reviewers: Laith Rastanawi
Report Upstream: N/A Work issues:
Branch: 9683151 (Commits, GitHub, GitLab) Commit: 96831516e18b4ecb50bf2ecf4e18f7056c9edd78
Dependencies: Stopgaps:

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Description

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.

Change History (7)

comment:1 Changed 15 months ago by gh-kliem

  • Authors set to Jonathan Kliem
  • Branch set to public/29073
  • Commit set to 29f9ebe6502ded976393f20fc5bcb1c2d5b846e8
  • Status changed from new to needs_review

New commits:

1db3349add notes about not echolonizing kernels for inexact rings
29f9ebedo not echolonize kernel basis for gale transpose

comment:2 Changed 15 months ago by git

  • Commit changed from 29f9ebe6502ded976393f20fc5bcb1c2d5b846e8 to cfd9b1a1d2aac511019d51068aa57921e5686703

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

cfd9b1afixed doc indent

comment:3 Changed 15 months ago by gh-LaisRast

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.

comment:4 Changed 15 months ago by git

  • Commit changed from cfd9b1a1d2aac511019d51068aa57921e5686703 to 96831516e18b4ecb50bf2ecf4e18f7056c9edd78

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

9683151better comment in doc of left_kernel

comment:5 Changed 15 months ago by gh-LaisRast

  • Status changed from needs_review to positive_review

comment:6 Changed 15 months ago by gh-LaisRast

  • Reviewers set to Laith Rastanawi

comment:7 Changed 15 months ago by vbraun

  • Branch changed from public/29073 to 96831516e18b4ecb50bf2ecf4e18f7056c9edd78
  • Resolution set to fixed
  • Status changed from positive_review to closed
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