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Implicitization using univariate resultants

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Abstract

Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univariate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing, 100049, China

    Liyong Shen

  2. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Chunming Yuan

Authors
  1. Liyong Shen
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  2. Chunming Yuan
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Correspondence to Liyong Shen.

Additional information

This project is supported by the Natural Science Foundation of China under Grant No. 10901163 and the Knowledge Innovation Program of the Chinese Academy of Sciences.

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Shen, L., Yuan, C. Implicitization using univariate resultants. J Syst Sci Complex 23, 804–814 (2010). https://doi.org/10.1007/s11424-010-7218-6

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  • DOI: https://doi.org/10.1007/s11424-010-7218-6

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