Expose some normaliz features

[jplab]

Using Normaliz can compute several things that are currently not interfaced. This ticket implements:

• Integral points generators
• Euclidean volume and volume
• Triangulation
• Hilbert series
• Ehrhart series of compact polyhedron
• Ehrhart quasi-polynomial of compact polyhedron

FOLLOWUP:

• Make ehrhart_polynomial uniform (in the spirit of .volume() that can have several engines.
• Move the lattice related methods to Polyhedra_normaliz_QQ.

Depends on #27682 Depends on #27716

CC: @videlec @mo271 @mkoeppe @sebasguts @w-bruns @braunmath @tscrim

Component: geometry

Keywords: polytope, normaliz, IMA-PolyGeom

Author: Jean-Philippe Labbé, Matthias Koeppe

Branch/Commit: da05706

Reviewer: Travis Scrimshaw, Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/25091

[jplab]

Branch: u/jipilab/normaliz_features

[jplab]

Commit: e421ff8

[jplab]

Dependencies: #22984, #25090

[jplab]

Last 10 new commits:

737552d	Updating patch with upstream fix for wrong number of lattice points.
530302d	Merge branch 'u/tscrim/upgrade_noramliz_pynormaliz-22984' of git://trac.sagemath.org/sage into u/tscrim/upgrade_noramliz_pynormaliz-22984
57d40b0	Upgrade Normaliz to 3.5.2.
6ba442d	Adding tests from [comment:24](#comment%3A24),25 of #22984.
183087a	Upgrade PyNormaliz to 1.12
7f47ec9	Adapted the polyhedron docstring
117e428	Upgrade normaliz to 3.5.3
7057ef4	Merge branch to get docstring adaptation
1b37e8b	Merge branch 'develop' into test_normaliz
e421ff8	First version of integral pts gen

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

Changed commit from e421ff8 to ac35212

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

b6ae686	Merge branch 'develop' of git://trac.sagemath.org/sage into t/25090/pynormaliz2
eaedcc2	Update PyNormaliz to 1.14
ac35212	Merge branch 'normaliz2' into normaliz_features

[jplab]

Changed branch from u/jipilab/normaliz_features to u/jipilab/some_normaliz_features

[jplab]

New commits:

bf8b172

Merge branch 'u/mkoeppe/pynormaliz2'

[jplab]

Changed commit from ac35212 to bf8b172

[jplab]

Changed commit from bf8b172 to 9a6af25

[jplab]

New commits:

4dbdc7d	Updated the Cone calls format
0257596	Merge branch 'pynormaliz2' into normaliz_features
9a6af25	Added volume, first version

[jplab]

Changed branch from u/jipilab/some_normaliz_features to public/some_normaliz_features

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

Changed commit from 9a6af25 to 3d3f64a

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

3d3f64a

Handle default behavior

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

Changed commit from 3d3f64a to f376748

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

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

1dcef4c	_init_from_normaliz_data: New, use it in _init_from_*representation
fcd8101	Updated pynormaliz to 1.15
f376748	Merge branch 'pynormaliz2' into normaliz_features

[videlec]

comment:7

Note that is_package_installed is being deprecated, see #20382

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Changed commit from f376748 to 55c9a04

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

55c9a04

Added Hilbert series

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

Changed commit from 55c9a04 to 720dc04

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

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

720dc04

Made tests pass

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

Changed commit from 720dc04 to a4ddeac

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

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

a4ddeac

Cropped feature methods

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

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

19d8539	Polyhedron_normaliz: In verbose mode, write out normaliz format files
4cfcd14	_normaliz_format: Fix last change
da8ae7a	Added data and cone methods to normaliz backend
44549fa	Merge branch 'pynormaliz2' into normaliz_features

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

Changed commit from a4ddeac to 44549fa

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Changed commit from 44549fa to e32c9fd

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

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

e32c9fd

Added triangulate with normaliz

[jplab]

Description changed:

--- 
+++ 
@@ -6,3 +6,5 @@
 - Triangulations

 This ticket provides some new features.
+
+TO DO: Make the bridge with PointConfiguration `triangulate` and the triangulation via normaliz.

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

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

45c39b8

Some small edits

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

Changed commit from e32c9fd to 45c39b8

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Changed commit from 45c39b8 to 5679821

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

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

5679821

Added handling the triangulation with point configurations

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

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

b045caf

Adapted inhomogeneous case

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

Changed commit from 5679821 to b045caf

[jplab]

Description changed:

--- 
+++ 
@@ -3,8 +3,5 @@
 - Integral points generators
 - Volume
 - Euclidean volume
-- Triangulations
-
-This ticket provides some new features.
-
-TO DO: Make the bridge with PointConfiguration `triangulate` and the triangulation via normaliz.
+- Triangulation
+- Hilbert series

[mkoeppe]

comment:18

It's probably best to add all lattice-point related methods to Polyhedron_QQ_normaliz rather than Polyhedron_normaliz in anticipation of #25097 (which moves integral_points and integral_hull there).

[jplab]

comment:19

Replying to @mkoeppe:

It's probably best to add all lattice-point related methods to Polyhedron_QQ_normaliz rather than Polyhedron_normaliz in anticipation of #25097 (which moves integral_points and integral_hull there).

I see. Yes I can do that.

[jplab]

comment:20

Replying to @jplab:

Replying to @mkoeppe:

It's probably best to add all lattice-point related methods to Polyhedron_QQ_normaliz rather than Polyhedron_normaliz in anticipation of #25097 (which moves integral_points and integral_hull there).

I see. Yes I can do that.

As discussed with mkoeppe: The move of the rational polyhedron methods will be done in #25097. The merge should go without conflicts.

[jplab]

comment:21

Replying to @videlec:

Note that is_package_installed is being deprecated, see #20382

Oh! Wow! Thanks for the timely warning! I set it as a dependency. I will change the check once it is merged...

[jplab]

Description changed:

--- 
+++ 
@@ -5,3 +5,5 @@
 - Euclidean volume
 - Triangulation
 - Hilbert series
+
+TODO: Adapt the `is_package_installed` for the volume part (see #20382).

[jplab]

Changed dependencies from #22984, #25090 to #22984, #25090, #20382

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Changed commit from b045caf to e7be14a

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

e7be14a

Fixed some polytopes and added some tests

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

Changed commit from e7be14a to 3615f8d

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

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

aa0e2ca	Merge branch normaliz3.5.3 and pynormaliz1.12 into sage8.2.rc2
2bbd8a6	Update normaliz and pynormaliz
82d7190	Merged old changes with latest versions
3615f8d	Merge branch 'update_py_normaliz' into normaliz_features

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Changed commit from 3615f8d to 8bff81f

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

e44cebd	Made tests pass for volume
8bff81f	Fixed the triangulation using normaliz

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

d0e2498

Added the Ehrhart Series and Quasi-Polynomial

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

Changed commit from 8bff81f to d0e2498

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

668fdfc

Added an example