Computational Synthetic Geometry (Paperback, 1989 ed.)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 1355
Release date:	July 1989
First published:	1989
Authors:	J urgen Bokowski • Bernd Sturmfels
Dimensions:	235 x 155 x 9mm (L x W x T)
Format:	Paperback
Pages:	172
Edition:	1989 ed.
ISBN-13:	978-3-540-50478-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > General Promotions
LSN:	3-540-50478-8
Barcode:	9783540504788

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