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Algorithms in Real Algebraic Geometry, Second Edition (Algorithms and Computation in Mathematics)

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Author(s): Saugata Basu, Richard Pollack, Marie-Francoise Roy,
Edition: 2nd
Year: 2006

Language: English
Pages: 672

front-matter......Page 1
1Introduction......Page 9
2Algebraically Closed Fields......Page 19
3Real Closed Fields......Page 36
4Semi-Algebraic Sets......Page 90
5Algebra......Page 107
6Decomposition of Semi-Algebraic Sets......Page 164
7Elements of Topology......Page 200
8Quantitative Semi-algebraic Geometry......Page 242
9Complexity of Basic Algorithms......Page 286
10Cauchy Index and Applications......Page 328
11Real Roots......Page 356
12Cylindrical Decomposition Algorithm......Page 407
13Polynomial System Solving......Page 449
14Existential Theory of the Reals......Page 508
15Quantifier Elimination......Page 536
16Computing Roadmaps and Connected Components of Algebraic Sets......Page 566
17Computing Roadmaps and Connected Components of Semi-algebraic Sets......Page 596
back-matter......Page 638