Computational Synthetic Geometry

Beschreibung

Neuware -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. 180 pp. Englisch.

Bestandsnummer des Verkäufers 9783540504788

Verkäufer kontaktieren

Diesen Artikel melden

Bibliografische Details

Titel

Computational Synthetic Geometry

Verlag

Springer Berlin Heidelberg, Springer Berlin Heidelberg Jul 1989

Erscheinungsjahr

1989

Sprache

Englisch

ISBN-10

3540504788

ISBN-13

9783540504788

Einband

Taschenbuch

Zustand

Neu

Abmessungen

235B x 155 H x 11 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 11 mm

Gewicht

283 Gramm

Über diesen Titel