Computing the Radical of an Ideal in Positive Characteristic

  • Authors:

  • Ryutaroh Matsumoto

  • Affiliations:

  • Tokyo Institute of Technology, Meguro-ku, Tokyo

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2001

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Abstract

We propose a method for computing the radical of an arbitrary ideal in the polynomial ring in n variables over a perfect field of characteristic p 0. In our method Buchberger's algorithm is performed once in n variables and a Gröbner basis conversion algorithm is performed at most npd times in 2 n variables, where d is the maximum of total degrees of generators of the ideal and 3. Next we explain how to compute radicals over a finitely generated coefficient field over a field K, when we have a radical computation method over the field K. Thus we can compute radicals over any finitely generated field over a perfect field.