Summary

Let I be an ideal in the polynomial ring k[x] over a field k. Saturation of I by the product x1 · · · xn, denoted by I: (x1 · · · xn) ∞ is the ideal {f: xa11 · · · xann f ∈ I, ai ≥ 0, 1 ≤ i ≤ n}. Binomials in the ring are defined as polynomials with at most two terms [1]. Ideals with a binomial basis are called binomial ideals. Toric ideals are examples of homogeneous binomial ideals. We describe a fast algorithm to compute the saturation, I: (x1 · · · xn)∞, of a homogeneous binomial ideal I. Here we would like to note that there are several algorithms to saturate pure difference binomial ideals, which are a special case of homogeneous binomial ideals, like the Sturmfels ’ saturation algorithm [3] and the Project and Lift algorithm [2]