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Quantifier Elimination and Cylindrical Algebraic Decomposition

  • Conference proceedings
  • © 1998

Overview

Editors:
  1. Bob F. Caviness

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

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  2. Jeremy R. Johnson

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

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  • 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
    Download chapter PDF

  2. Introduction

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

  3. Quantifier Elimination by Cylindrical Algebraic Decomposition — Twenty Years of Progress

    • George E. Collins
    Pages 8-23

  4. A Decision Method for Elementary Algebra and Geometry

    • Alfred Tarski
    Pages 24-84

  5. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition

    • George E. Collins
    Pages 85-121

  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

  9. An Improvement of the Projection Operator in Cylindrical Algebraic Decomposition

    • Hoon Hong
    Pages 166-173

  10. Partial Cylindrical Algebraic Decomposition for Quantifier Elimination

    • George E. Collins, Hoon Hong
    Pages 174-200

  11. Simple Solution Formula Construction in Cylindrical Algebraic Decomposition Based Quantifier Elimination

    • Hoon Hong
    Pages 201-219

  12. Recent Progress on the Complexity of the Decision Problem for the Reals

    • James Renegar
    Pages 220-241

  13. An Improved Projection Operation for Cylindrical Algebraic Decomposition

    • Scott McCallum
    Pages 242-268

  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

  16. Characterizations of the Macaulay Matrix and Their Algorithmic Impact

    • Georg Hagel
    Pages 317-326

  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

  20. A Combinatorial Algorithm Solving Some Quantifier Elimination Problems

    • Laureano González-Vega
    Pages 365-375
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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.

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

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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