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Tracing a planar algebraic curve

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Abstract

In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of the real roots of several univariate polynomials.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei

    Chen Falai, Feng Yuyu & Jerenj Kozak

  2. Department of Mathematics, University of Science and Technology of China, 230026, Hefei

    Chen Falai, Feng Yuyu & Jerenj Kozak

  3. Department of Mathemetics, University of Ljubljana, 61000, Ljubljana, Slovenia

    Chen Falai, Feng Yuyu & Jerenj Kozak

Authors
  1. Chen Falai
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  2. Feng Yuyu
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  3. Jerenj Kozak
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Additional information

Supported by NSF and SF of National Educational Committee of China.

Suppotred in part by ICTP, and in part by NSF and SF of National Educational Committee of China.

Supported by the Ministry of Science and Technology of Slovenia.

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Falai, C., Yuyu, F. & Kozak, J. Tracing a planar algebraic curve. Appl. Math. Chin. Univ. 12, 15–24 (1997). https://doi.org/10.1007/s11766-997-0002-2

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  • DOI: https://doi.org/10.1007/s11766-997-0002-2

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