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Item Details
Title: COMPUTATIONAL SYNTHETIC GEOMETRY
By: Jurgen Bokowski, Bernd Sturmfels
Format: Paperback

List price: £22.99


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ISBN 10: 3540504788
ISBN 13: 9783540504788
Publisher: SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG
Pub. date: 12 July, 1989
Edition: 1989 ed.
Series: Lecture Notes in Mathematics No. 1355
Pages: 172
Description: 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 and vector geometries from incidence structures.
Synopsis: 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.
Illustrations: biography
Publication: Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Returns: Returnable
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ALGEBRAIC STATISTICS FOR COMPUTATIONAL BIOLOGY
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APPLICATIONS OF COMPUTATIONAL ALGEBRAIC GEOMETRY (HB)
COMBINATORIAL ALGEBRAIC GEOMETRY (HB)
COMBINATORIAL COMMUTATIVE ALGEBRA (HB)
COMBINATORIAL COMMUTATIVE ALGEBRA (PB)
GEOMETRIC COMBINATORICS (HB)
GROBNER BASES AND CONVEX POLYTOPES (PB)
GROBNER DEFORMATIONS OF HYPERGEOMETRIC DIFFERENTIAL EQUATIONS (HB)
GROBNER DEFORMATIONS OF HYPERGEOMETRIC DIFFERENTIAL EQUATIONS (PB)
INTRODUCTION TO TROPICAL GEOMETRY
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INVITATION TO NONLINEAR ALGEBRA
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LECTURES ON ALGEBRAIC STATISTICS (PB)
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