Computational Oriented Matroids: Equivalence Classes of Matrices within a Natural Framework
Cambridge University Press, 5/8/2006
EAN 9780521849302, ISBN10: 0521849306
Hardcover, 338 pages, 24.7 x 17.4 x 2.5 cm
Language: English
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.
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.
'For illustrative purposes, the book contains not only a large number of colorful pictures of oriented matroids, but also pictures of artwork, by various artists, all having oriented matroid themes; the book, itself, is perhaps a piece of art.' Zentralblatt MATH