Solving systems of algebraic equations

  • Hidetsune Kobayashi
  • Shuichi Moritsugu
  • Robert W. Hogan
Gröbner Bases
Part of the Lecture Notes in Computer Science book series (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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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Hidetsune Kobayashi
    • 1
  • Shuichi Moritsugu
    • 2
  • Robert W. Hogan
    • 3
  1. 1.Dept. of Math.,College of Sci. & Tech.Nihon Univ.TokyoJapan
  2. 2.Dept. of Inform. Sci.,Faculty of Sci.Univ. of TokyoTokyoJapan
  3. 3.CITIZEN WATCH Co., Ltd.Tokorozawa-shi,SaitamaJapan

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