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Cylindrical algebraic decomposition by quantifier elimination

  • Dennis S. Arnon
  • Scott McCallum
6. Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 144)

Abstract

Cylindrical algebraic decompositions were introduced as a major component of a new quantifier elimination algorithm for elementary algebra and geometry (G. Collins, 1973). In the present paper we turn the tables and show that one can use quantifier elimination for elementary algebra and geometry to obtain a new version of the cylindrical algebraic decomposition algorithm. A key part of our result is a theorem, of interest in its own right. that relates the multiplicities of the roots of a polynomial to their continuity.

Keywords

Real Root Computer Science Department Elementary Algebra Quantifier Elimination Real Closed Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Arnon DS: Algorithms for the geometry of semi-algebraic sets, Ph.D. Dissertation, Technical Report #436, Computer Science Department, University of Wisconsin Madison, 1981.Google Scholar
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    Collins GE: Quantifier elimination for real closed fields by cylindrical algebraic decomposition, in Second Gl Conference on Automata Theory and Formal Languages, vol. 33 of Lecture Notes in Computer Science, Springer-Verlag, Berlin. 1975, pp 134–183.Google Scholar
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    Collins GE: Quantifier elimination for real closed fields by cylindrical algebraic decomposition — a synopsis, SIGSAM Bulletin of the ACM 10, 1 (1976), pp 10–12.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Dennis S. Arnon
    • 1
  • Scott McCallum
    • 2
  1. 1.Computer Science DepartmentPurdue UniversityWest LafayetteUSA
  2. 2.Computer Science DepartmentUniversity of Wisconsin - MadisonMadisonUSA

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