Efficient resolution of singularities of plane curves

  • Dexter Kozen
Invited Talk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 880)

Abstract

We give a new algorithm for resolving singularities of plane curves. The algorithm is polynomial time in the bit complexity model, does not require factorization, and works over (ℚ) or finite fields.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Ben-Or, D. Kozen, and J. Reif, The complexity of elementary algebra and geometry, J. Comput. Syst. Sci., 32 (1985), pp. 251–264. Invited special issue.Google Scholar
  2. 2.
    G. A. Bliss, Algebraic Functions, Amer. Math. Soc., 1933.Google Scholar
  3. 3.
    C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, American Mathematical Society, 1951.Google Scholar
  4. 4.
    A. L. Chistov, Polynomial complexity of the Newton-Puiseux algorithm, in Math. Found. Comput. Sci., vol. 233 of Lect. Notes. Comput. Sci., Springer, 1986, pp. 247–255.Google Scholar
  5. 5.
    C. Dicrescenzo and D. Duval, Computations on curves, vol. 174 of Lect. Notes in Comput. Sci., Springer, 1984, pp. 100–107.Google Scholar
  6. 6.
    -Algebraic computations on algebraic numbers, in Informatique et Calcul, Wiley-Masson, 1985, pp. 54–61.Google Scholar
  7. 7.
    W. Fulton, Algebraic Curves, Addison Wesley, 1989.Google Scholar
  8. 8.
    D. Ierardi and D. Kozen, Parallel resultant computation, in Synthesis of Parallel Algorithms, J. Reif, ed., Morgan Kaufmann, 1993, pp. 679–720.Google Scholar
  9. 9.
    S. Landau, Factoring polynomials over algebraic number fields, SIAM J. Comput., 14 (1985), pp. 184–195.Google Scholar
  10. 10.
    S. Lang, Introduction to Algebraic and Abelian Functions, Springer-Verlag, second ed., 1972.Google Scholar
  11. 11.
    A. K. Lenstra, Factoring polynomials over algebraic number fields, in Proc. EuroCal 1983, vol. 162 of Lect. Notes in Comput. Sci., Springer, 1983, pp. 245–254.Google Scholar
  12. 12.
    A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann., 261 (1982), pp. 515–534.Google Scholar
  13. 13.
    J. Teitelbaum, The computational complexity of the resolution of plane curve singularities, Math. Comp., 54 (1990), pp. 797–837.Google Scholar
  14. 14.
    B. M. Trager. Personal communication, 1994.Google Scholar
  15. 15.
    B. M. Trager, Integration of Algebraic Functions, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, September 1984.Google Scholar
  16. 16.
    P. G. Walsh, The Computation of Puiseux Expansions and a Quantitative Version of Runge's Theorem on Diophantine Equations, PhD thesis, University of Waterloo, 1994.Google Scholar
  17. 17.
    R. Zippel. Personal communication, 1994.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Dexter Kozen
    • 1
  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA

Personalised recommendations