A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots

  • Authors:

  • Göran Björck;Ralf Fröberg

  • Affiliations:

  • Department of Mathematics, Stockholm University, Box 6701, S-113 85 Stockholm, Sweden;Department of Mathematics, Stockholm University, Box 6701, S-113 85 Stockholm, Sweden

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 1991

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Abstract

This paper deals with the problem of using symbolic algebra to count the solutions of inhomogeneous systems of algebraic equations. A trick is presented whereby the faster algorithms for the homogeneous case can be used in the inhomogeneous case. The method is applied to the cyclic n-roots studied by one of the authors (and sometimes referred to as solutions to Amborg's system or Davenport's problem).