Algorithms in Real Algebraic Geometry

  • Saugata Basu
  • Richard Pollack
  • Marie-Franco̧ise Roy

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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 1-8
  3. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 9-24
  4. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 25-72
  5. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 73-89
  6. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 91-136
  7. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 137-172
  8. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 173-200
  9. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 201-240
  10. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 241-282
  11. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 283-319
  12. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 321-363
  13. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 365-419
  14. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 421-463
  15. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 465-492
  16. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 493-521
  17. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 523-547
  18. Saugata Basu, Richard Pollack, Marie-Francoise Roy
    Pages 549-585
  19. Back Matter
    Pages 587-602

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, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. 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.

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-Franco̧ise 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/10.1007/978-3-662-05355-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-05357-7
  • Online ISBN 978-3-662-05355-3
  • Series Print ISSN 1431-1550
  • About this book