2023/08/14 by Taylor Brysiewicz, Brysiewicz, Taylor, Michael Joswig +1
Computer Science · #52-04 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2308.07459
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number theory). Assuming little familiarity with the subject, we give an introduction to computations in polyhedral geometry using OSCAR, as a chapter of the upcoming OSCAR book. 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.