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 |
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I made some changes to the code of |
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Documentation preview for this PR (built with commit 2a9328a; changes) is ready! 🎉 |
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Corrected typo
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looks good. Let us wait for the continuous integration
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sagemathgh-39496: Add deformation cones and checking for regularity for 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
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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