Computing the primary decomposition of zero-dimensional ideals

  • Authors:

  • Chris Monico

  • Affiliations:

  • Department of Mathematics, University of Notre Dame, Notre Dame, IN

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2002

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Abstract

Let K be an infinite perfect computable field and let I ⊆ K[x] be a zero-dimensional ideal represented by a Gröbner basis. We derive a new algorithm for computing the reduced primary decomposition of I using only standard linear algebra and univariate polynomial factorization techniques. In practice, the algorithm generally works in finite fields of large characteristic as well.