© 1998

Quantifier Elimination and Cylindrical Algebraic Decomposition

  • Bob F. Caviness
  • Jeremy R. Johnson


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

Conference proceedings

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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Bob F. Caviness, Jeremy R. Johnson
    Pages 1-7
  3. Michael J. Fischer, Michael O. Rabin
    Pages 122-135
  4. Dennis S. Arnon, George E. Collins, Scott McCallum
    Pages 136-151
  5. Dennis S. Arnon, George E. Collins, Scott McCallum
    Pages 152-165
  6. J. R. Johnson
    Pages 269-299
  7. L. González-Vega, T. Recio, H. Lombardi, M.-F. Roy
    Pages 300-316
  8. Hoon Hong, J. Rafael Sendra
    Pages 327-340
  9. Saugata Basu, Richard Pollack, Marie-Françoise Roy
    Pages 341-350
  10. Daniel Richardson
    Pages 351-364

About these proceedings


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.


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

Editors and affiliations

  • Bob F. Caviness
    • 1
  • Jeremy R. Johnson
    • 2
  1. 1.Department of Computer and Information SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of Mathematics and Computer ScienceDrexel UniversityPhiladelphiaUSA

Bibliographic information


"... 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