Finding binomials in polynomial ideals

07/07/2016

∙

by   Anders Jensen, et al.

∙

0

∙

share

We describe an algorithm which finds binomials in a given ideal I⊂Q[x_1,...,x_n] and in particular decides whether binomials exist in I at all. Binomials in polynomial ideals can be well hidden. For example, the lowest degree of a binomial cannot be bounded as a function of the number of indeterminates, the degree of the generators, or the Castelnuovo--Mumford regularity. We approach the detection problem by reduction to the Artinian case using tropical geometry. The Artinian case is solved with algorithms from computational number theory.