Minkowski Addition of Polytopes PDF Download

Author: Peter Gritzmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 62

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Author: P. Gritzmann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Peter Gritzmann
Publisher:
ISBN:
Category : Convex polytopes
Languages : de
Pages : 54

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Author: DIMACS (GROUP)
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 32

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Using the Minkowski addition of Newton polytopes, we show that the following problem can be solved in polynomial time for any finite set of polynomials [formula], where d is fixed: Does there exist a term order [tau] such that [Tau] is a Gröbner basis for its ideal with respect to [tau]? If not, find an optimal term order for [Tau] with respect to a natural Hilbert function criterion."

Author: Bernd Sturmfels
Publisher: American Mathematical Soc.
ISBN: 0821804871
Category : Mathematics
Languages : en
Pages : 176

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This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

Author: Tibor Bisztriczky
Publisher: Springer Science & Business Media
ISBN: 9401109249
Category : Mathematics
Languages : en
Pages : 515

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The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Author: Günter M. Ziegler
Publisher: Springer Science & Business Media
ISBN: 1461384311
Category : Mathematics
Languages : en
Pages : 347

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Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1498711421
Category : Computers
Languages : en
Pages : 1928

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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Author: Ralf Fröberg
Publisher: John Wiley & Sons
ISBN: 9780471974420
Category : Mathematics
Languages : en
Pages : 198

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Book Description
Grobner-Basen werden von Mathematikern und Informatikern zunehmend fur eine breite Palette von Anwendungen genutzt, in denen die algorithmische algebraische Geometrie eine Rolle spielt. Hier werden Grobner-Basen von einem konstruktiven, wenig abstrakten Standpunkt aus behandelt, wobei nur geringe Vorkenntnisse in linearer Algebra und komplexen Zahlen vorausgesetzt werden; zahlreiche Beispiele helfen bei der Durchdringung des Stoffes. Mit einer Ubersicht uber aktuell erhaltliche relevante Softwarepakete.

Author: Rolf Schneider
Publisher: Cambridge University Press
ISBN: 1107601010
Category : Mathematics
Languages : en
Pages : 759

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Book Description
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.