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Algorithms in Real Algebraic Geometry

Algorithms in Real Algebraic Geometry PDF Author: Saugata Basu
Publisher: Springer Science & Business Media
ISBN: 3662053551
Category : Mathematics
Languages : en
Pages : 602

Book Description
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Algorithms in Real Algebraic Geometry

Algorithms in Real Algebraic Geometry PDF Author: Saugata Basu
Publisher: Springer Science & Business Media
ISBN: 3662053551
Category : Mathematics
Languages : en
Pages : 602

Book Description
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Algorithms in Real Algebraic Geometry

Algorithms in Real Algebraic Geometry PDF Author: Saugata Basu
Publisher: Springer Science & Business Media
ISBN: 3540330992
Category : Mathematics
Languages : en
Pages : 665

Book Description
This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.

Computing in Algebraic Geometry

Computing in Algebraic Geometry PDF Author: Wolfram Decker
Publisher: Springer Science & Business Media
ISBN: 3540289925
Category : Mathematics
Languages : en
Pages : 331

Book Description
This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Real Algebraic Geometry

Real Algebraic Geometry PDF Author: Michel Coste
Publisher: Springer
ISBN: 3540473378
Category : Mathematics
Languages : en
Pages : 425

Book Description
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.

Algorithmic Algebra

Algorithmic Algebra PDF Author: Bhubaneswar Mishra
Publisher: Springer Science & Business Media
ISBN: 1461243440
Category : Computers
Languages : en
Pages : 427

Book Description
Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

Semidefinite Optimization and Convex Algebraic Geometry

Semidefinite Optimization and Convex Algebraic Geometry PDF Author: Grigoriy Blekherman
Publisher: SIAM
ISBN: 1611972280
Category : Mathematics
Languages : en
Pages : 487

Book Description
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Computations in Algebraic Geometry with Macaulay 2

Computations in Algebraic Geometry with Macaulay 2 PDF Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 9783540422303
Category : Mathematics
Languages : en
Pages : 354

Book Description
This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Using Algebraic Geometry

Using Algebraic Geometry PDF Author: David A. Cox
Publisher: Springer Science & Business Media
ISBN: 1475769113
Category : Mathematics
Languages : en
Pages : 513

Book Description
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

Lectures in Real Geometry

Lectures in Real Geometry PDF Author: Fabrizio Broglia
Publisher: Walter de Gruyter
ISBN: 3110811111
Category : Mathematics
Languages : en
Pages : 285

Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

A First Course in Computational Algebraic Geometry

A First Course in Computational Algebraic Geometry PDF Author: Wolfram Decker
Publisher: Cambridge University Press
ISBN: 1107612535
Category : Computers
Languages : en
Pages : 127

Book Description
A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.