Computational Oriented Matroids
Equivalence Classes of Matrices within a Natural Framework
Seiten
2006
Cambridge University Press (Verlag)
978-0-521-84930-2 (ISBN)
Cambridge University Press (Verlag)
978-0-521-84930-2 (ISBN)
The combination of concrete applications and computation, the profusion of illustations, and the large number of examples and exercises will make this an ideal introductory text on the subject.. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
Juergen Bokowski is a Professor of Mathematics at Darmstadt University of Technology
1. Geometric matrix models i; 2. Geometric matrix models ii; 3. From matrices to rank 3 oriented matroids; 4. Oriented matroids of arbitrary rank; 5. From oriented matroids to face lattices; 6. From face lattices to oriented matroids i; 7. From face lattices to oriented matroids ii; 8. From oriented matroids to matrices; 9. Computational synthetic geometry; 10. Some oriented matroid applications; 11. Some inttrinsic oriented matroid problems; Bibliography; Index.
| Erscheint lt. Verlag | 8.5.2006 |
|---|---|
| Zusatzinfo | 50 Halftones, unspecified; 150 Line drawings, unspecified; 81 Line drawings, color |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 180 x 255 mm |
| Gewicht | 960 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 0-521-84930-6 / 0521849306 |
| ISBN-13 | 978-0-521-84930-2 / 9780521849302 |
| Zustand | Neuware |
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