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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
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.
G. A. Bliss, Algebraic Functions, Amer. Math. Soc., 1933.
C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, American Mathematical Society, 1951.
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.
C. Dicrescenzo and D. Duval, Computations on curves, vol. 174 of Lect. Notes in Comput. Sci., Springer, 1984, pp. 100–107.
-Algebraic computations on algebraic numbers, in Informatique et Calcul, Wiley-Masson, 1985, pp. 54–61.
W. Fulton, Algebraic Curves, Addison Wesley, 1989.
D. Ierardi and D. Kozen, Parallel resultant computation, in Synthesis of Parallel Algorithms, J. Reif, ed., Morgan Kaufmann, 1993, pp. 679–720.
S. Landau, Factoring polynomials over algebraic number fields, SIAM J. Comput., 14 (1985), pp. 184–195.
S. Lang, Introduction to Algebraic and Abelian Functions, Springer-Verlag, second ed., 1972.
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.
A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann., 261 (1982), pp. 515–534.
J. Teitelbaum, The computational complexity of the resolution of plane curve singularities, Math. Comp., 54 (1990), pp. 797–837.
B. M. Trager. Personal communication, 1994.
B. M. Trager, Integration of Algebraic Functions, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, September 1984.
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.
R. Zippel. Personal communication, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kozen, D. (1994). Efficient resolution of singularities of plane curves. In: Thiagarajan, P.S. (eds) Foundation of Software Technology and Theoretical Computer Science. FSTTCS 1994. Lecture Notes in Computer Science, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58715-2_109
Download citation
DOI: https://doi.org/10.1007/3-540-58715-2_109
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58715-6
Online ISBN: 978-3-540-49054-8
eBook Packages: Springer Book Archive