. "Theses"@en . . . . . . . . . . . . "e-book [online only]"@en . . "Electronic books"@en . "Electronic books" . . . . . . "Computational Synthetic Geometry" . . "Computational Synthetic Geometry"@en . . . . . . . . . "Llibres electrònics" . . . . . . . . . . . . . . . . . . . "Computational synthetic geometry"@en . . "Computational synthetic geometry" . . . . . . . . . "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."@en . "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." . . . . . . . . . . . "Synthetische Geometrie" . . "Geometrie." . . "Algoritmi." . . "Informàtica aplicada Geometria." . . . . "Berechenbarkeit" . . "Processament de dades." . . "Geometrie Datenverarbeitung." . . "géométrie combinatoire." . . "Geometría algebraica." . . "Geometria computacional." . . "Analisi combinatoria." . . "polytopes convexes." . . "Géométrie Informatique." . . "Geometrieverarbeitung." . . "Geometrija." . . "Matroidi - Teoria." . . "Algorithmische Geometrie" . . "Algorithmische Geometrie." . "Datenverarbeitung." . . "Geometry Data processing." . . "Geometry Data Processing." . "SpringerLink (Service en ligne)" . . "Computer" . . "Matemàtica." . . "Geometria Processament de dades." . . "Geometria adatfeldolgozás." . . "Konvexitás." . . "Geometria" . . "Geometria proiettiva." . . "Berechenbare Geometrie." . .