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 polytope
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1355 Jurqen Bokowski
Bernd Sturmfels
Computational Synthetic Geometry
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1355 Jurqen Bokowski
Bernd Sturmfels
Computational Synthetic Geometry
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Authors
Jurgen Bokowski University of Darmstadt, Department of Mathematics SchloBgartenstr. 7,6100 Darmstadt, Federal Republic of Germany e-mail: XBR1DBON@ DDATHD21.bitnet Bernd Sturmfels Cornell University, Department of Mathematics Ithaca, New York 14853, USA
Mathematics Subject Classification (1980): 05B35, 14M 15,51 A20, 52A25, 68C20, 68E99 ISBN 3-540-50478-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-50478-8 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 Printed on acid-free paper
Preface 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 polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. We show that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. For many special cases practical symbolic algorithms are presented and discussed. The methods developed are applied to obtain new mathematical results on polytopes, projective configurations and the combinatorics of Grassmann varieties. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and it will serve professional geometers and computer scientists as an introduction and motivation for further research. For several years both authors have had a fruitful and enjoyable collaboration which culminates in the present work. The first five chapters of this monograph are essentially Bernd Sturmfels' 1987 Ph.D. thesis which was supervised by Victor Klee at the University of Washington, Seattle. Chapter VI was written jointly by both authors, while the remaining chapters were written by Jiirgen Bokowski in 1988. The first author thanks all of his students who have helped to m
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