A lot of polytope constructors are broken

[videlec]

A lot of polytopes constructors in sage.geometry.polyhedron.library. For example

1. The Rhombicuboctahedron does not return what it should (as Python division was thought as Sage integer divisions). There is in the code

verts = [ [-3/2, -1/2, -1/2], [-3/2, -1/2, 1/2], [-3/2, 1/2, -1/2],
...

2. The great_rhombicuboctahedron is defined over QQ but it should be defined over QQ[sqrt(2)]! There are in two places rough approximation of sqrt(2) in the code

v1 = QQ(131739771357/54568400000)   # ~ sqrt(2) + 1 but actually 2 due to Python division
v2 = QQ(104455571357/27284200000)   # ~ 2 sqrt(2) but actually 3 due to Python division

Instead, we should use the base_ring argument (with appropriate defaults) and use base_ring(2).sqrt() instead.

3. The functions unrelated to construction of Polytopes are moved out of the class Polytopes:
   • Polytopes.orthonormal_1, Polytopes.project_1 will be renamed respectively zero_sum_projection and project_points
   • the one line Polytopes._pfunc is just removed

While we're at it, remove the deprecations from #11634.

During the process I discovered two annoying bugs:

• 18214 Bug in volume computation of polyhedron

• 18220 Bug when creating a polyhedron with coefficients in RR

  Moreover, we can get a great speed up with the following because many polytopes have now coordinates in a quadratic number fields:

• 18215: Huge speed up for hash of quadratic number field elements

• 18226: Native _mpfr_ method on quadratic number field elements

Depends on #18211

CC: @nathanncohen

Component: geometry

Author: Vincent Delecroix

Branch/Commit: a58da00

Reviewer: Nathann Cohen

Issue created by migration from https://trac.sagemath.org/ticket/18213

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

comment:39

Okayyyyyyyyyyyyyy. End of the review. Nothing else to add ;-)

Very good job. This code needed to be cleaned, and it is much better now.

But please, next time: smaller patches. You waste your reviewers' health :-P

Nathann

[videlec]

comment:40

Replying to @nathanncohen:

HMmmmmmmm... I don't exactly know what the isometry group is, but let's try anyway: what about defining a complete graph on your points, in which each edge has a color associated to its length. Wouldn't the automorphism group of that be what you want?

That is a valid definition. But the standard one is the set of orthogonal matrices that preserve the polyhedron. And it would be nice for isometry_group to be a finite matrix group (and not permutations)!

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from fac3cff to 1a82754

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

21e70a7	Trac 18213: review commit
1a82754	Trac 18213: doctest fix

[videlec]

comment:42

Patchbot should be happy after that.

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

comment:43

Some broken doctests in the patchbot's report. Also, can you be sure that the sqrt(6.) / factorial(5) are not subject to numerical noise? There is no #tol on them right now.

Nathann

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

comment:44

Hmmmmmm.. I can't seem to find on google an implementation of an isometry group function anywhere O_o

[a1031e5c-5e2c-4c90-8ba4-91be67e304df]

comment:45

Hi Vincent and Nathann

Just a quick comment, as I'm not sure how useful this will be for general polyhedra: There is a method for lattice polytopes: LatticePolytope_PPL (in sage.geometry.polyhedron.ppl_lattice_polytope) has a method lattice_automorphism_group()

Cheers, Jan

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

120c1e9	Trac 18213: more abs tol in doctests
d09d8a5	Trac 18211: forgot a # optional in the doctest
a58da00	Trac 18213: merge failed doctest from #18211

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 1a82754 to a58da00

[videlec]

comment:48

Replying to @nathanncohen:

Some broken doctests in the patchbot's report. Also, can you be sure that the sqrt(6.) / factorial(5) are not subject to numerical noise? There is no #tol on them right now.

I don't know... Patchbot did not complain about this.

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

comment:50

Okayyyyyyy. Then positive_review!

Nathann

[6bdad4c1-1e26-4f2f-a442-a01a2292c181]

Reviewer: Nathann Cohen

[vbraun]

Changed branch from u/vdelecroix/18213 to a58da00