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Add deformation cones and checking for regularity for Point Configurations and normal fans of Polyhedra #39496
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I still need to add the method |
I made some changes to the code of |
Documentation preview for this PR (built with commit 2a9328a; changes) is ready! 🎉 |
Corrected typo
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looks good. Let us wait for the continuous integration
…or Point Configurations and normal fans of Polyhedra In this pull request, we add the method `deformation_cone` (to point configurations and polyhedron) and `is_polytopal` (to fans). This is related to the Kahler cone of Toric Varieties, but has some subtle differences to make it work as it should in the discrete geometry context. Therefore, it has a separate implementation. TODO: In the future, perhaps it could be fusioned. ```sage sage: tc = Polyhedron([(1, -1), (1/3, 1), (1, 1/3), (-1, 1), (-1, -1)]) sage: dc = tc.deformation_cone() sage: dc.an_element() (2, 1, 1, 0, 0) sage: [_.A() for _ in tc.Hrepresentation()] [(1, 0), (0, 1), (0, -1), (-3, -3), (-1, 0)] sage: P = Polyhedron(rays=[(1, 0, 2), (0, 1, 1), (0, -1, 1), (-3, -3, 0), (-1, 0, 0)]) sage: P.rays() (A ray in the direction (-1, -1, 0), A ray in the direction (-1, 0, 0), A ray in the direction (0, -1, 1), A ray in the direction (0, 1, 1), A ray in the direction (1, 0, 2)) sage: py = Polyhedron([(0, -1, -1), (0, -1, 1), (0, 1, -1), (0, 1, 1), (1, 0, 0)]) sage: dc_py = py.deformation_cone(); dc_py A 4-dimensional polyhedron in QQ^5 defined as the convex hull of 1 vertex, 1 ray, 3 lines sage: [ineq.b() for ineq in py.Hrepresentation()] [0, 1, 1, 1, 1] sage: r = dc_py.rays()[0] sage: l1,l2,l3 = dc_py.lines() sage: r.vector()-l1.vector()/2-l2.vector()-l3.vector()/2 (0, 1, 1, 1, 1) ``` ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. URL: sagemath#39496 Reported by: JP Labbe Reviewer(s): Frédéric Chapoton
In this pull request, we add the method
deformation_cone
(to point configurations and polyhedron) andis_polytopal
(to fans).This is related to the Kahler cone of Toric Varieties, but has some subtle differences to make it work as it should in the discrete geometry context. Therefore, it has a separate implementation.
TODO: In the future, perhaps it could be fusioned.
📝 Checklist