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Real Roots

  • Saugata Basu
  • Richard Pollack
  • Marie-Francoise Roy
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 10)

Abstract

In Section 1 we describe classical bounds on the roots of polynomials. In Section 2 we study real roots of univariate polynomials by a method based on Descartes’s law of sign and Bernstein polynomials. These roots are characterized by intervals with rational endpoints. The method presented works only for archimedean real closed fields. In the second part of the chapter we study exact methods working in general real closed fields. Section 3 is devoted to exact sign determination in a real closed field and Section 4 to characterizations of roots in a real closed field.

Keywords

Real Root Binary Complexity Great Common Divisor Bernstein Polynomial Univariate Polynomial 
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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Bibliographical Notes

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    M. Coste, M.-F. Roy, Thom’s lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets. Journal of Symbolic Computation 5, No.1/2, 121–129 (1988).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Saugata Basu
    • 1
  • Richard Pollack
    • 2
  • Marie-Francoise Roy
    • 3
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA
  3. 3.IRMAR Campus de BeaulieuUniversité de Rennes IRennes cedexFrance

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