The Resource Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book)
Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book)
Resource Information
The item Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semialgebraic set appear frequently in many areas of science and engineering. In this firstever 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, and researchers in computer science and engineering will find the required mathematical background. Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semialgebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 662 pages)
 Note
 Textbook for graduates
 Contents

 Introduction
 1 Algebraically Closed Fields
 2 Real Closed Fields
 3 SemiAlgebraic Sets
 4 Algebra
 5 Decomposition of SemiAlgebraic Sets
 6 Elements of Topology
 7 Quantitative SemiAlgebraic Geometry
 8 Complexity of Basic Algorithms
 9 Cauchy Index and Applications
 10 Real Roots
 11 Cylindrical Decomposition Algorithm
 12 Polynomial System Solving
 13 Existential Theory of the Reals
 14 Quantifier Elimination
 15 Computing Roadmaps and Connected Components of Algebraic Sets
 16 Computing Roadmaps and Connected Components of SemiAlgebraic Sets
 References
 Index of Notation
 Index
 Isbn
 9783540330998
 Label
 Algorithms in real algebraic geometry
 Title
 Algorithms in real algebraic geometry
 Statement of responsibility
 Saugata Basu, Richard Pollack, MarieFrançoise Roy
 Language
 eng
 Summary
 The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semialgebraic set appear frequently in many areas of science and engineering. In this firstever 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, and researchers in computer science and engineering will find the required mathematical background. Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semialgebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 1968
 http://library.link/vocab/creatorName
 Basu, Saugata
 Dewey number
 516.3/5
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA564
 LC item number
 .B38 2006eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Pollack, Richard
 Roy, M.F.
 Series statement
 Algorithms and computation in mathematics,
 Series volume
 v. 10
 http://library.link/vocab/subjectName

 Geometry, Algebraic
 Algorithms
 Algorithms
 Geometry, Algebraic  Data processing
 Label
 Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book)
 Note
 Textbook for graduates
 Bibliography note
 Includes bibliographical references (pages 587593)and indexes
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1 Algebraically Closed Fields  2 Real Closed Fields  3 SemiAlgebraic Sets  4 Algebra  5 Decomposition of SemiAlgebraic Sets  6 Elements of Topology  7 Quantitative SemiAlgebraic Geometry  8 Complexity of Basic Algorithms  9 Cauchy Index and Applications  10 Real Roots  11 Cylindrical Decomposition Algorithm  12 Polynomial System Solving  13 Existential Theory of the Reals  14 Quantifier Elimination  15 Computing Roadmaps and Connected Components of Algebraic Sets  16 Computing Roadmaps and Connected Components of SemiAlgebraic Sets  References  Index of Notation  Index
 Control code
 SPR262692707
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 662 pages)
 Form of item
 online
 Isbn
 9783540330998
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations.
 Specific material designation
 remote
 Label
 Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book)
 Note
 Textbook for graduates
 Bibliography note
 Includes bibliographical references (pages 587593)and indexes
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1 Algebraically Closed Fields  2 Real Closed Fields  3 SemiAlgebraic Sets  4 Algebra  5 Decomposition of SemiAlgebraic Sets  6 Elements of Topology  7 Quantitative SemiAlgebraic Geometry  8 Complexity of Basic Algorithms  9 Cauchy Index and Applications  10 Real Roots  11 Cylindrical Decomposition Algorithm  12 Polynomial System Solving  13 Existential Theory of the Reals  14 Quantifier Elimination  15 Computing Roadmaps and Connected Components of Algebraic Sets  16 Computing Roadmaps and Connected Components of SemiAlgebraic Sets  References  Index of Notation  Index
 Control code
 SPR262692707
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 662 pages)
 Form of item
 online
 Isbn
 9783540330998
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations.
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/AlgorithmsinrealalgebraicgeometrySaugata/iVv9m6Zq5w/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/AlgorithmsinrealalgebraicgeometrySaugata/iVv9m6Zq5w/">Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, MarieFrançoise Roy, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>