Name: computational synthetic geometry
SKU: 3485212
Price: 30.93 EUR
Availability: InStock
Author: bokowski,sturmfels

portada computational synthetic geometry

Type

Physical Book

Publisher

Springer

Author

bokowski,sturmfels

Language

English

Pages

168

ISBN

3540504788

ISBN13

9783540504788

Synopsis "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 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.