Overview

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. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Full Product Details

Author:   Saugata Basu ,  Richard Pollack ,  Marie-Francoise Roy
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1st ed. 2003
ISBN:  

9783540280200

ISBN 10:   3540280200
Pages:   602
Publication Date:   15 October 2020
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   CD-ROM
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

0 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.

Reviews

.,. The book under review gives a self-contained account of some of the more recent and important algorithms arising in RAG [real algebraic geometry]. ... This material has mostly appeared in other sources; however, it is very nice to have it all in one book. ...the book is wonderful reference for algorithms in RAG, for the expert and non-expert alike. <p>V.Powers, Mathematical Reviews Clippings from Issue 2004g

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