Ebook: Algorithms in Real Algebraic Geometry

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Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-8
Algebraically Closed Fields....Pages 9-24
Real Closed Fields....Pages 25-72
Semi-Algebraic Sets....Pages 73-89
Algebra....Pages 91-136
Decomposition of Semi-Algebraic Sets....Pages 137-172
Elements of Topology....Pages 173-200
Quantitative Semi-algebraic Geometry....Pages 201-240
Complexity of Basic Algorithms....Pages 241-282
Cauchy Index and Applications....Pages 283-319
Real Roots....Pages 321-363
Polynomial System Solving....Pages 365-419
Cylindrical Decomposition Algorithm....Pages 421-463
Existential Theory of the Reals....Pages 465-492
Quantifier Elimination....Pages 493-521
Computing Roadmaps and Connected Components of Algebraic Sets....Pages 523-547
Computing Roadmaps and Connected Components of Semi-algebraic Sets....Pages 549-585
Back Matter....Pages 587-602

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Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-8
Algebraically Closed Fields....Pages 9-24
Real Closed Fields....Pages 25-72
Semi-Algebraic Sets....Pages 73-89
Algebra....Pages 91-136
Decomposition of Semi-Algebraic Sets....Pages 137-172
Elements of Topology....Pages 173-200
Quantitative Semi-algebraic Geometry....Pages 201-240
Complexity of Basic Algorithms....Pages 241-282
Cauchy Index and Applications....Pages 283-319
Real Roots....Pages 321-363
Polynomial System Solving....Pages 365-419
Cylindrical Decomposition Algorithm....Pages 421-463
Existential Theory of the Reals....Pages 465-492
Quantifier Elimination....Pages 493-521
Computing Roadmaps and Connected Components of Algebraic Sets....Pages 523-547
Computing Roadmaps and Connected Components of Semi-algebraic Sets....Pages 549-585
Back Matter....Pages 587-602
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