Jürgen Bokowski

(Author)

Computational Synthetic Geometry (1989)Paperback - 1989, 12 July 1989

Computational Synthetic Geometry (1989)
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Part of Series
Lecture Notes in Mathematics
Print Length
172 pages
Language
English
Publisher
Springer
Date Published
12 Jul 1989
ISBN-10
3540504788
ISBN-13
9783540504788

Description

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.

Product Details

Authors:
Jürgen BokowskiBernd Sturmfels
Book Edition:
1989
Book Format:
Paperback
Country of Origin:
DE
Date Published:
12 July 1989
Dimensions:
23.39 x 15.6 x 0.97 cm
ISBN-10:
3540504788
ISBN-13:
9783540504788
Language:
English
Location:
Berlin, Heidelberg
Pages:
172
Publisher:
Weight:
258.55 gm

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