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25 Remote Warehouse Mathematics- Algebraic Geometry

This title in other editions

Algorithms and Computation in Mathematics #10: Algorithms in Real Algebraic Geometry

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Algorithms and Computation in Mathematics #10: Algorithms in Real Algebraic Geometry Cover

 

Synopses & Reviews

Publisher Comments:

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 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. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added.

Synopsis:

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.

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.

Product Details

ISBN:
9783540330981
Author:
Basu, Saugata
Publisher:
Springer
Author:
Pollack, Richard
Author:
Roy, Marie-Frangoise
Author:
Coste-Roy, Marie-Franoise
Author:
Roy, Marie-Frangoise
Author:
Coste-Roy, Marie-Françoise
Author:
Roy, Marie-Francoise
Subject:
Computer Science
Subject:
Geometry - Algebraic
Subject:
Programming - Algorithms
Subject:
polynomial system solving
Subject:
quantifier elimination
Subject:
real root counting
Subject:
Road maps
Subject:
semi-algebraic set
Subject:
Algebraic Geometry
Subject:
Algorithms
Subject:
Symbolic and Algebraic Manipulation
Subject:
Symbolic and Algebraic Manipulation <P>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 informa
Subject:
Mathematics-Algebraic Geometry
Copyright:
Edition Number:
2
Edition Description:
2nd ed. 2006
Series:
Algorithms and Computation in Mathematics
Series Volume:
10
Publication Date:
20060821
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
672
Dimensions:
235 x 155 mm 2460 gr

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Algorithms and Computation in Mathematics #10: Algorithms in Real Algebraic Geometry New Hardcover
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Product details 672 pages Springer - English 9783540330981 Reviews:
"Synopsis" by , 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.
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