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Algorithms in Real Algebraic Geometry

Author: Saugata Basu; Richard Pollack; M -F Roy
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003.
Series: Algorithms and computation in mathematics, 10.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Saugata Basu; Richard Pollack; M -F Roy
ISBN: 9783662053553 3662053551
OCLC Number: 851368312
Language Note: English.
Description: 1 online resource (viii, 602 pages).
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 Polynomial System Solving --
12 Cylindrical decomposition algorithm --
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.
Series Title: Algorithms and computation in mathematics, 10.
Responsibility: by Saugata Basu, Richard Pollack, Marie-Franco̧ise Roy.

Abstract:

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. 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.

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