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Algorithms in Real Algebraic Geometry.

Author: Arjeh M Cohen; Henri Cohen; David Eisenbud
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
Series: Algorithms and computation in mathematics, 10.
Edition/Format:   eBook : Document : English : Second edition
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, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real  Read more...
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Genre/Form: Electronic books
Material Type: Document
Document Type: Book, Computer File
All Authors / Contributors: Arjeh M Cohen; Henri Cohen; David Eisenbud
ISBN: 3642069649 9783642069642 3540330984 9783540330981
OCLC Number: 990548366
Language Note: English.
Description: 1 online resource (664 pages).
Contents: ""Table of 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 Cylindrical Decomposition Algorithm""; ""12 Polynomial System Solving""; ""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 of Notation""; ""Index""
Series Title: Algorithms and computation in mathematics, 10.
Other Titles: Algorithms and Computation in Mathematics, Volume 10

Abstract:

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  Read more...

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From the reviews:"The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. ... In general, the monograph is well written and will be useful both for Read more...

 
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