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Complexity of the computation of cylindrical decomposition and topology of real algebraic curves using Thom's lemma

  • M.-F. Roy
  • A. Szpirglas
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1420)

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References

  1. [A H U]
    A. Aho, J. Hopcroft, J. Ullman: The design and analysis of computer algorithms. Addison Wesley, Reading (1974).zbMATHGoogle Scholar
  2. [A McC]
    D. Arnon, S. McCallum: A polynomial-time algorithm for the topological type of a real algebraic curve. J. of Symbolic Computation 5 213–236 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [C,R]
    M. Coste, M.-F. Roy: Thom's lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets. J. of Symbolic computation 5 121–130 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [GLRR]
    L.Gonzalez, H. Lombardi, T.Recio, M.-F. Roy: Specialisation de la suite de Sturm et sous-résultants. To appear in RAIRO Informatique théorique.Google Scholar
  5. [GT]
    P. Gianni, C. Traverso: Shape determination of real curves and surfaces. Ann. Univ. Ferrara SezVII Sec. Math. vol XXIX 87–109 (1983).MathSciNetzbMATHGoogle Scholar
  6. [K]
    M. Kac: On the average number of real roots of a random algebraic equation. Bull. Amer. Math. soc. 49 (1943).Google Scholar
  7. [Loos]
    R. Loos: Generalized polynomial remainder sequences. In Computer algebra, symbolic and algebraic computation. Springer Verlag, Berlin (1982).CrossRefzbMATHGoogle Scholar
  8. [Mi]
    M. Mignotte: Some useful bounds. In Computer algebra, symbolic and algebraic computation. Springer Verlag, Berlin (1982).CrossRefzbMATHGoogle Scholar
  9. [R]
    M.-F. Roy: Computation of the topology of a real algebraic curve. To appear in Computational geometry and topology, Congress in Sevilla 1987.Google Scholar
  10. [RS]
    M.-F. Roy, A. Szpirglas: Complexity of the computation on real algebraic numbers. To appear in the Journal of Symbolic Computation.Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • M.-F. Roy
    • 1
  • A. Szpirglas
    • 2
  1. 1.Université de Rennes IFrance
  2. 2.Université Paris-NordFrance

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