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European Computer Algebra Conference

EUROCAM 1982: Computer Algebra pp 215–222Cite as

Cylindrical algebraic decomposition by quantifier elimination

  • 6. Algorithms III
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((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.

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References

  1. 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 

  2. Brown WS, Traub JF: On Euclid's algorithm and the theory of subresultants, J. Assoc. Comp. Mach., 18, 4 (1971), pp 505–514.

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  3. 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.

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  4. 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.

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  5. Marden M: Geometry of polynomials, (second edn.). American Mathematical Society, Providence, 1966.

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  6. Tarski A: A decision method for elementary algebra and geometry, University of California Press, 1948; second edn., rev. 1951.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Purdue University, 47907, West Lafayette, Indiana, USA

    Dennis S. Arnon

  2. Computer Science Department, University of Wisconsin - Madison, 53706, Madison, Wisconsin, USA

    Scott McCallum

Authors
  1. Dennis S. Arnon
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  2. Scott McCallum
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Editor information

Jacques Calmet

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© 1982 Springer-Verlag Berlin Heidelberg

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Arnon, D.S., McCallum, S. (1982). Cylindrical algebraic decomposition by quantifier elimination. In: Calmet, J. (eds) Computer Algebra. EUROCAM 1982. Lecture Notes in Computer Science, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11607-9_25

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  • DOI: https://doi.org/10.1007/3-540-11607-9_25

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11607-3

  • Online ISBN: 978-3-540-39433-4

  • eBook Packages: Springer Book Archive

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