Advertisement

Solving systems of algebraic equations by using gröbner bases

  • Michael Kalkbrener
Polynomial Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 378)

Abstract

In this paper we give an explicit description of an algorithm for finding all solutions of a system of algebraic equations which is solvable and has finitely many solutions. This algorithm is an improved version of a method which was deviced by B. Buchberger. By a theorem proven in this paper, gcd-computations occurring in Buchberger's method can be avoided in our algorithm.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Buchberger: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes Math. 4/3, 374–383 (1970)CrossRefGoogle Scholar
  2. [2]
    B. Buchberger: Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory, in Recent Trends in Multidimensional Systems Theory, N.K. Bose (ed.), D. Reidel Publ. Comp. 184–232 (1985)Google Scholar
  3. [3]
    D. Lazard: Ideal Bases and Primary Decomposition: Case of Two Variables, J. of Symbolic Computation 1, 261–270 (1985)Google Scholar
  4. [4]
    W. Trinks: Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen, J. of Number Theory 10/4, 475–488 (1978)CrossRefGoogle Scholar
  5. [5]
    B.L. van der Waerden: Algebra II, Springer-Verlag (1967)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Michael Kalkbrener
    • 1
  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler Universität LinzAustria

Personalised recommendations