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The topological configuration of a real algebraic curve

  • Takis Sakkalis (a1)
Abstract

This paper presents an algorithm, motivated by Morse Theory, for the topological configuration of the components of a real algebraic curve {f(x, y) = 0}. The running time of the algorithm is O(n12 (d + log n)2 log n), where n, d are the degree and maximum coefficient size of f(x, y).

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References
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[l]Arnborg, S. and Feng, H., ‘Algebraic decomposition of regular curves’, J. Symbolic Comput. 5 (1988), 131140.
[2]Arnon, D.S., ‘Topologically reliable display of algebraic curves’, Computer Graphics 17 (1983), 219227.
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[10]Sakkalis, T., An algorithmic application of Morse theory to real algebraic geometry, Ph.D. Dissertation (University of Rochester, 1986).
[11]Sakkalis, T., ‘The Euclidean algorithm and the degree of the Gauss map’, SIAM J. Comput. 19 (1990), 538543.
[12]Sakkalis, T., ‘On the zeros of a polynomial vector field’, IBM TR, RC 13303 (1987).
[13]Sakkalis, T. and Farouki, R., ‘Singular points of algebraic curves’, J. Symbolic Comput. 9 (1990), 405421.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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