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The Resource Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, Marie-Françoise Roy, (electronic book)

Algorithms in real algebraic geometry, Saugata Basu, Richard Pollack, Marie-Françoise Roy, (electronic book)

Label
Algorithms in real algebraic geometry
Title
Algorithms in real algebraic geometry
Statement of responsibility
Saugata Basu, Richard Pollack, Marie-Françoise Roy
Creator
Contributor
Subject
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 semi-algebraic set appear frequently in many areas of science and engineering. 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, and 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 revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
Member of
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, Marie-Françoise Roy, (electronic book)
Instantiates
Publication
Note
Textbook for graduates
Bibliography note
Includes bibliographical references (pages 587-593)-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 Semi-Algebraic Sets -- 4 Algebra -- 5 Decomposition of Semi-Algebraic Sets -- 6 Elements of Topology -- 7 Quantitative Semi-Algebraic 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 Semi-Algebraic 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, Marie-Françoise Roy, (electronic book)
Publication
Note
Textbook for graduates
Bibliography note
Includes bibliographical references (pages 587-593)-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 Semi-Algebraic Sets -- 4 Algebra -- 5 Decomposition of Semi-Algebraic Sets -- 6 Elements of Topology -- 7 Quantitative Semi-Algebraic 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 Semi-Algebraic 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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