Algorithms in Real Algebraic Geometry

  • Saugata Basu
  • Richard Pollack
  • Marie-Françoise Roy

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 10)

Table of contents

About this book

Introduction

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.

Keywords

algorithms complexity geometry polynomial system solving quantifier elimination real root counting roadmaps semi-algebraic set sets

Authors and affiliations

  • Saugata Basu
    • 1
  • Richard Pollack
    • 2
  • Marie-Françoise Roy
    • 3
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA
  3. 3.IRMAR Campus de BeaulieuUniversité de Rennes IRennes cedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-33099-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-33098-1
  • Online ISBN 978-3-540-33099-8
  • Series Print ISSN 1431-1550
  • About this book