Computational Synthetic Geometry

Name: Computational Synthetic Geometry
Brand: Springer, Berlin
SKU: 9783540504788
Price: 25.23 EUR
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Autor: Jürgen Bokowski, Bernd Sturmfels

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer, Berlin

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Computational synthetic geometry deals with methods for realizing abstract geometric objects in conc...

Informácie o knihe

Autor

Jürgen Bokowski, Bernd Sturmfels

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Stránok

172

EAN

9783540504788

ISBN

3540504788

Enbook ID

01565141

Vydavateľ

Springer, Berlin

Hmotnosť

290

Rozmery

155 x 235 x 9

Kompletný popis

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.

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Computational Synthetic Geometry

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