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)


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.


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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

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