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International Symposium on Symbolic and Algebraic Computation

ISSAC 1988: Symbolic and Algebraic Computation pp 139–149Cite as

Solving systems of algebraic equations

  • Gröbner Bases
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 358))

Abstract

This paper shows an algorithm for computing all the solutions with their multiplicities of a system of algebraic equations. The algorithm previously proposed by the authors for the case where the ideal is zero-dimensional and radical seems to have practical efficiency. We present a new method for solving systems which are not necessarily radical. The set of all solutions is partitioned into subsets each of which consists of mutually conjugate solutions having the same multiplicity.

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References

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Author information

Authors and Affiliations

  1. Dept. of Math.,College of Sci. & Tech., Nihon Univ., Chiyoda-ku, 101, Tokyo, Japan

    Hidetsune Kobayashi

  2. Dept. of Inform. Sci.,Faculty of Sci., Univ. of Tokyo, Bunkyo-ku, 113, Tokyo, Japan

    Shuichi Moritsugu

  3. CITIZEN WATCH Co., Ltd., 359, Tokorozawa-shi,Saitama, Japan

    Robert W. Hogan

Authors
  1. Hidetsune Kobayashi
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  2. Shuichi Moritsugu
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  3. Robert W. Hogan
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Editor information

P. Gianni

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© 1989 Springer-Verlag Berlin Heidelberg

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Kobayashi, H., Moritsugu, S., Hogan, R.W. (1989). Solving systems of algebraic equations. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_13

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  • DOI: https://doi.org/10.1007/3-540-51084-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51084-0

  • Online ISBN: 978-3-540-46153-1

  • eBook Packages: Springer Book Archive

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