Polyhedral And Algebraic Methods In Computational Geometry

Polyhedral And Algebraic Methods In Computational Geometry Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Polyhedral And Algebraic Methods In Computational Geometry book. This book definitely worth reading, it is an incredibly well-written.

Polyhedral and Algebraic Methods in Computational Geometry

Nik Pachis
Polyhedral and Algebraic Methods in Computational Geometry Book PDF

Author : Nik Pachis
Publisher : Unknown
Page : 250 pages
File Size : 47,8 Mb
Release : 2016-04-01
Category : Electronic
ISBN : 1681174499

Get Book

Polyhedral and Algebraic Methods in Computational Geometry by Nik Pachis Pdf

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with history stretching back to antiquity. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. Other important applications of computational geometry include robotics, geographic information systems, integrated circuit design, computer-aided engineering, and computer vision. Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. This book is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Polyhedral and Algebraic Methods in Computational Geometry

Michael Joswig,Thorsten Theobald
Polyhedral and Algebraic Methods in Computational Geometry Book PDF

Author : Michael Joswig,Thorsten Theobald
Publisher : Springer
Page : 250 pages
File Size : 46,8 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 1447148185

Get Book

Polyhedral and Algebraic Methods in Computational Geometry by Michael Joswig,Thorsten Theobald Pdf

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Polyhedral and Algebraic Methods in Computational Geometry

Michael Joswig,Thorsten Theobald
Polyhedral and Algebraic Methods in Computational Geometry Book PDF

Author : Michael Joswig,Thorsten Theobald
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 50,7 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9781447148173

Get Book

Polyhedral and Algebraic Methods in Computational Geometry by Michael Joswig,Thorsten Theobald Pdf

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Computational Geometry of Positive Definite Quadratic Forms

Achill Schurmann
Computational Geometry of Positive Definite Quadratic Forms Book PDF

Author : Achill Schurmann
Publisher : American Mathematical Soc.
Page : 183 pages
File Size : 43,5 Mb
Release : 2009
Category : Discrete geometry
ISBN : 9780821847350

Get Book

Computational Geometry of Positive Definite Quadratic Forms by Achill Schurmann Pdf

"Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Gebhard Böckle,Wolfram Decker,Gunter Malle
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book PDF

Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 53,7 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668

Get Book

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by Gebhard Böckle,Wolfram Decker,Gunter Malle Pdf

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Combinatorial and Computational Geometry

Jacob E. Goodman,Janos Pach,Emo Welzl
Combinatorial and Computational Geometry Book PDF

Author : Jacob E. Goodman,Janos Pach,Emo Welzl
Publisher : Cambridge University Press
Page : 640 pages
File Size : 42,7 Mb
Release : 2005-08-08
Category : Computers
ISBN : 0521848628

Get Book

Combinatorial and Computational Geometry by Jacob E. Goodman,Janos Pach,Emo Welzl Pdf

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Handbook of Discrete and Computational Geometry

Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Handbook of Discrete and Computational Geometry Book PDF

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 43,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

Get Book

Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

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.

Discrete Geometry

Andras Bezdek
Discrete Geometry Book PDF

Author : Andras Bezdek
Publisher : CRC Press
Page : 500 pages
File Size : 42,7 Mb
Release : 2003-02-04
Category : Mathematics
ISBN : 9780824747619

Get Book

Discrete Geometry by Andras Bezdek Pdf

Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.

A Primer of Algebraic Geometry

Huishi Li,Freddy Van Oystaeyen
A Primer of Algebraic Geometry Book PDF

Author : Huishi Li,Freddy Van Oystaeyen
Publisher : CRC Press
Page : 392 pages
File Size : 52,6 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781351990950

Get Book

A Primer of Algebraic Geometry by Huishi Li,Freddy Van Oystaeyen Pdf

"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."

Real Algebraic Geometry and Optimization

Thorsten Theobald
Real Algebraic Geometry and Optimization Book PDF

Author : Thorsten Theobald
Publisher : American Mathematical Society
Page : 312 pages
File Size : 44,6 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470474317

Get Book

Real Algebraic Geometry and Optimization by Thorsten Theobald Pdf

This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.

Essentials of Tropical Combinatorics

Michael Joswig
Essentials of Tropical Combinatorics Book PDF

Author : Michael Joswig
Publisher : American Mathematical Society
Page : 398 pages
File Size : 54,8 Mb
Release : 2021-12-08
Category : Mathematics
ISBN : 9781470467418

Get Book

Essentials of Tropical Combinatorics by Michael Joswig Pdf

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

Nonlinear Computational Geometry

Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald
Nonlinear Computational Geometry Book PDF

Author : Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 55,9 Mb
Release : 2009-10-28
Category : Mathematics
ISBN : 9781441909992

Get Book

Nonlinear Computational Geometry by Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald Pdf

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Commutative Algebra

Alberto Corso
Commutative Algebra Book PDF

Author : Alberto Corso
Publisher : CRC Press
Page : 128 pages
File Size : 44,5 Mb
Release : 2017-08-09
Category : Electronic
ISBN : 1138402125

Get Book

Commutative Algebra by Alberto Corso Pdf

Packed with contributions from international experts, Commutative Algebra: Geometric, Homological, Combinatorial, and Computational Aspects features new research results that borrow methods from neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation, and topology. This book consists of articles presented during two conferences held in Spain and Portugal in June, 2003. It encompasses a variety of topics, including blowup algebras, Castelnuovo-Mumford regularity, integral closure and normality, Koszul homology, liaison theory, multiplicities, polarization, and reductions of ideals. This comprehensive volume will stimulate further research in the field.

Computing the Continuous Discretely

Matthias Beck,Sinai Robins
Computing the Continuous Discretely Book PDF

Author : Matthias Beck,Sinai Robins
Publisher : Springer
Page : 285 pages
File Size : 48,9 Mb
Release : 2015-11-14
Category : Mathematics
ISBN : 9781493929696

Get Book

Computing the Continuous Discretely by Matthias Beck,Sinai Robins Pdf

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Advances in Discrete and Computational Geometry

Bernard Chazelle,Jacob E. Goodman,Richard Pollack
Advances in Discrete and Computational Geometry Book PDF

Author : Bernard Chazelle,Jacob E. Goodman,Richard Pollack
Publisher : American Univ in Cairo Press
Page : 484 pages
File Size : 50,8 Mb
Release : 1999
Category : Mathematics
ISBN : 0821806742

Get Book

Advances in Discrete and Computational Geometry by Bernard Chazelle,Jacob E. Goodman,Richard Pollack Pdf

This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, "Discrete and Computational Geometry: Ten Years Later", held in 1996 at Mt. Holyoke College (So.Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.