An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection

  • Authors:

  • Isabel Bermejo;Ignacio García-Marco;Juan José Salazar-González

  • Affiliations:

  • Facultad de Matemáticas, Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain;Facultad de Matemáticas, Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain;Facultad de Matemáticas, Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2007

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Abstract

Let K be an arbitrary field and {d"1,...,d"n} a set of all-different positive integers. The aim of this work is to propose and evaluate an algorithm for checking whether or not the toric ideal of the affine monomial curve {(t^d^"^1,...,t^d^"^n)|t@?K}@?A"K^n is a complete intersection. The algorithm is based on new results regarding the toric ideal of the curve, and it can be seen as a generalization of the classical result of Herzog for n=3. Computational experiments show that the algorithm is able to solve large-size instances.