Advertisement

Keywords

Symmetric Function Real Zero Real Point Geometric Point Conjugate Pair 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BCR 1987]
    Bochnak, J., M. Coste, M-F. Roy: “Géométrie algebrique réelle”, Springer Verlag, Berlin (1987).Google Scholar
  2. [Cau 1815]
    Cauchy, A. L.: “Sur la Détermination du nombre des Racines réelles dans les Équations algébriques”, Journal de L'École Polytechnique, Cahier 17, Tome X, Paris (1815).Google Scholar
  3. [Gan 1977]
    Gantmacher, F. R.: “The Theory of Matrices, vol I., Chelsea Publishing Company, New York, NY (1977).Google Scholar
  4. [Her 1852]
    Hermite, C.: “Sur L'Extension du Théorème de M. Sturm a un Système D'Équations Simultanées”, Comptes rendus des s'eances de l'Académie des Sciences, tome XXXV, 1852.Google Scholar
  5. [Ioh 1982]
    Iohovidov, S. I.: “Hankel and Toeplitz Matrices and Forms”, Birkhäuser, (1982).Google Scholar
  6. [Mac 1902]
    Macaulay, F. S.: “Some Formulae in Elimination”, Proceedings of the London Mathematical Society, (1) 33 (1903), 3–27.Google Scholar
  7. [Mil 1990]
    Milne, P.: “On the Solutions of a Set of Polynomial Equations”, (unpublished preprint), Bath University (1990).Google Scholar
  8. [P 1991]
    Pedersen, P.: “Calculating multidimensional symmetric functions using Jacobi's formula”, Proc. AAECC (1991).Google Scholar
  9. [P 1991a]
    Pedersen, P.: “Counting Real Zeros”, thesis New York University (1991).Google Scholar
  10. [Ren 1989]
    Renegar, J.: “On the Computational Complexity and Geometry of the First-Order Theory of the Reals”, parts I–III, Cornell School of Operations Research and Industrial Engineering (ORIE) tech reports 853,854,856 (1989).Google Scholar
  11. [Stu 1904]
    Sturm, C.: “Über die Auflösung der Numerischen Gleichungen (1835)”, in the series “Ostwald's Klassiker der Exacten Wissenschaften”, Nr. 143, Wilhelm Engelmann, Leipzig (1904).Google Scholar
  12. [Tar 1951]
    Tarski, A.: “A Decision Method for Elementary Algebra and Geometry”, University of California Press, Berkeley (1951).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Paul Pedersen
    • 1
  1. 1.New York UniversityUSA

Personalised recommendations