Computational Synthetic Geometry

  • Authors
  • Jürgen Bokowski
  • Bernd Sturmfels
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1355)

Table of contents

  1. Front Matter
    Pages I-IV
  2. Jürgen Bokowski, Bernd Sturmfels
    Pages 1-17
  3. Jürgen Bokowski, Bernd Sturmfels
    Pages 18-31
  4. Jürgen Bokowski, Bernd Sturmfels
    Pages 32-60
  5. Jürgen Bokowski, Bernd Sturmfels
    Pages 61-86
  6. Jürgen Bokowski, Bernd Sturmfels
    Pages 87-101
  7. Jürgen Bokowski, Bernd Sturmfels
    Pages 102-114
  8. Jürgen Bokowski, Bernd Sturmfels
    Pages 115-132
  9. Jürgen Bokowski, Bernd Sturmfels
    Pages 133-146
  10. Jürgen Bokowski, Bernd Sturmfels
    Pages 147-157
  11. Back Matter
    Pages 158-168

About this book

Introduction

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.

Keywords

Mathematica Microsoft Access Processing Vector space boundary element method complexity computer algebra construction discrete geometry eXist field knowledge manifold mathematics theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0089253
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50478-8
  • Online ISBN 978-3-540-46013-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book