Computing lattice ideals of unions of monomial curves

In this paper we present a combinatorial study of binomial ideals of dimension 1 of k[X1,…,Xn], using monomial parametrizations of the irreducible affine curves defined by their associated primes. We find an algorithm that checks whether or not the ideal of a union of monomial curves is binomial and another one that calculates curves such that their associated ideal is a prescribed lattice ideal.