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Assuming little familiarity with the subject, we give an introduction to computations in polyhedral geometry using OSCAR. In particular, we define polytopes, polyhedra, and polyhedral fans, and we give a brief overview about computing convex hulls and solving linear programs. Three detailed case studies are left for experts in polyhedral geometry. These are concerned with face numbers of random polytopes, constructions and properties of Gelfand–Tsetlin polytopes, and secondary polytopes.

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Polyhedral Geometry

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  • 发表日期：

    2025年

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  • Taylor Brysiewicz,
  • Michael Joswig

摘要

Assuming little familiarity with the subject, we give an introduction to computations in polyhedral geometry using OSCAR. In particular, we define polytopes, polyhedra, and polyhedral fans, and we give a brief overview about computing convex hulls and solving linear programs. Three detailed case studies are left for experts in polyhedral geometry. These are concerned with face numbers of random polytopes, constructions and properties of Gelfand–Tsetlin polytopes, and secondary polytopes.