Computational synthetic geometry /
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 geometrie...
| Main Author: | |
|---|---|
| Corporate Author: | |
| Other Authors: | |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
[1989]
|
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1355. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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. |
|---|---|
| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (168 pages) : illustrations (some color). |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 158-166) and index. |
| ISBN: | 9783540460138 (electronic bk.) 3540460136 (electronic bk.) |
| ISSN: | 0075-8434 ; |