Computational Synthetic Geometry / by Jürgen Bokowski, Bernd Sturmfels.

Format:

Book

Author/Creator:

Bokowski, Jürgen, author.

Sturmfels, Bernd, 1962- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1355.

Lecture Notes in Mathematics, 0075-8434 ; 1355

Language:

English

Subjects (All):

Geometry.

Local Subjects:

Geometry.

Physical Description:

1 online resource (VIII, 172 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.

System Details:

text file PDF

Summary:

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.

Contents:

Preliminaries

On the existence of algorithms

Combinatorial and algebraic methods

Algebraic criteria for geometric realizability

Geometric methods

Recent topological results

Preprocessing methods

On the finding of polyheadral manifolds

Matroids and chirotopes as algebraic varieties.

Other Format:

Printed edition:

ISBN:

9783540460138

Access Restriction:

Restricted for use by site license.