Algorithms in Real Algebraic Geometry / Edition 2

Algorithms in Real Algebraic Geometry / Edition 2

by Saugata Basu, Richard Pollack, Marie-Francoise Roy
     
 

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ISBN-10: 3540330984

ISBN-13: 9783540330981

Pub. Date: 08/21/2006

Publisher: Springer Berlin Heidelberg

This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being

Overview

This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. 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 second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.

Product Details

ISBN-13:
9783540330981
Publisher:
Springer Berlin Heidelberg
Publication date:
08/21/2006
Series:
Algorithms and Computation in Mathematics Series, #10
Edition description:
2nd ed. 2006
Pages:
662
Product dimensions:
9.21(w) x 6.14(h) x 1.50(d)

Table of Contents

Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity of Basic Algorithms.- Cauchy Index and Applications.- Real Roots.- Cylindrical Decomposition Algorithm.- Polynomial System Solving.- Existential Theory of the Reals.- Quantifier Elimination.- Computing Roadmaps and Connected Components of Algebraic Sets.- Computing Roadmaps and Connected Components of Semi-algebraic Sets.

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