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Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics, V. 10)

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The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. 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 ivaluable parts of it, to undergraduate students.

Author(s): Saugata Basu, Richard Pollack, Marie-Françoise Roy
Series: Algorithms and Computation in Mathematics, V. 10
Edition: 1
Publisher: Springer
Year: 2003

Language: German
Pages: 664

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