Computational Synthetic Geometry / Jürgen Bokowski, Bernd Sturmfels

• Autore: Bokowski, Jürgen
• Pubblicazione: Berlin, : Springer, 1989
• Descrizione fisica: viii, 172 p. ; 24 cm
• Soggetto topico: 05-XX - Combinatorics [MSC 2020]; 05B35 - Combinatorial aspects of matroids and geometric lattices [MSC 2020]; 14M15 - Grassmannians, Schubert varieties, flag manifolds [MSC 2020]; 51A20 - Configuration theorems in linear incidence geometry [MSC 2020]; 51D20 - Combinatorial geometries and geometric closure systems [MSC 2020]; 52Bxx - Polytopes and polyhedra [MSC 2020]; 68Rxx - Discrete mathematics in relation to computer science [MSC 2020]; 68W30 - Symbolic computation and algebraic computation [MSC 2020]
• Soggetto non controllato: Boundary Element Methods; Complexity; Computer Algebra; Constructions; Discrete geometry; Fields; Knowledge; Manifolds; Mathematica; Mathematics; Microsoft Access; Processing; Vector spaces; eXist
• Altri autori: Sturmfels, Bernd
• Nota di contenuto: Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.
• Titolo autorizzato: Computational synthetic geometry
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00265716
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: https://doi.org/10.1007/BFb0089253