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Book cover
  • Conference proceedings
  • © 1998

Quantifier Elimination and Cylindrical Algebraic Decomposition

Editors:

  1. Bob F. Caviness

    1. Department of Computer and Information Sciences, University of Delaware, Newark, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Jeremy R. Johnson

    1. Department of Mathematics and Computer Science, Drexel University, Philadelphia, USA

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    You can also search for this editor in PubMed   Google Scholar

  • The book serves as an introduction and survey of the field of algorithmic quantifier elimination

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (20 papers)

  1. Front Matter

    Pages i-xix
    PDF

  2. Introduction

    • Bob F. Caviness, Jeremy R. Johnson
    Pages 1-7

  6. Super-Exponential Complexity of Presburger Arithmetic

    • Michael J. Fischer, Michael O. Rabin
    Pages 122-135

  7. Cylindrical Algebraic Decomposition I: The Basic Algorithm

    • Dennis S. Arnon, George E. Collins, Scott McCallum
    Pages 136-151

  8. Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane

    • Dennis S. Arnon, George E. Collins, Scott McCallum
    Pages 152-165

  14. Algorithms for Polynomial Real Root Isolation

    • J. R. Johnson
    Pages 269-299

  15. Sturm—Habicht Sequences, Determinants and Real Roots of Univariate Polynomials

    • L. González-Vega, T. Recio, H. Lombardi, M.-F. Roy
    Pages 300-316

  17. Computation of Variant Resultants

    • Hoon Hong, J. Rafael Sendra
    Pages 327-340

  18. A New Algorithm to Find a Point in Every Cell Defined by a Family of Polynomials

    • Saugata Basu, Richard Pollack, Marie-Françoise Roy
    Pages 341-350

  19. Local Theories and Cylindrical Decomposition

    • Daniel Richardson
    Pages 351-364
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About this book

George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the-art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.
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Keywords

  • Algebraic Computation
  • Symbolic Computation
  • Symbolisches Rechnen
  • Variable
  • algorithms
  • calculus
  • complexity
  • geometry
  • proof
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Reviews

"... The book is a nearly complete presentation of the history of the developement of CAD algorithms and its applications, and is suitable for the beginner as well as the expert ...” Zentralblatt für Mathematik
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Editors and Affiliations

  • Department of Computer and Information Sciences, University of Delaware, Newark, USA

    Bob F. Caviness

  • Department of Mathematics and Computer Science, Drexel University, Philadelphia, USA

    Jeremy R. Johnson

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Bibliographic Information

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Access via your institution

Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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