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Three kinds of extraneous factors in Dixon resultants

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Abstract

Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    ShiZhong Zhao

  2. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    HongGuang Fu

  3. Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, 610041, China

    HongGuang Fu

Authors
  1. ShiZhong Zhao
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  2. HongGuang Fu
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Corresponding author

Correspondence to ShiZhong Zhao.

Additional information

This work was supported by the National Key Basic Special Funds of China (Grant No. 2004CB318003), the Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KJCX2-YW-S02), the National Natural Science Foundation of China (Grant No. 90718041), Shanghai Leading Academic Discipline Project (Grant No. B412) and the Doctor Startup Foundation of East China Normal University (Grant No. 790013J4)

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Zhao, S., Fu, H. Three kinds of extraneous factors in Dixon resultants. Sci. China Ser. A-Math. 52, 160–172 (2009). https://doi.org/10.1007/s11425-008-0094-z

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  • DOI: https://doi.org/10.1007/s11425-008-0094-z

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