Skip to main content
  • Book
  • © 1989

Computational Synthetic Geometry

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

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (9 chapters)

  1. Front Matter

    Pages I-IV
  2. Preliminaries

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 1-17
  3. On the existence of algorithms

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 18-31
  4. Combinatorial and algebraic methods

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 32-60
  5. Algebraic criteria for geometric realizability

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 61-86
  6. Geometric methods

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 87-101
  7. Recent topological results

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 102-114
  8. Preprocessing methods

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 115-132
  9. On the finding of polyhedral manifolds

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 133-146
  10. Matroids and chirotopes as algebraic varieties

    • Jürgen Bokowski, Bernd Sturmfels
    Pages 147-157
  11. Back Matter

    Pages 158-168

About this book

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

  • Book Title: Computational Synthetic Geometry

  • Authors: Jürgen Bokowski, Bernd Sturmfels

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089253

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-50478-8Published: 12 July 1989

  • eBook ISBN: 978-3-540-46013-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 172

  • Topics: Geometry

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions