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

Let K be an arbitrary field and {d1,…,dn} 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 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.