  We describe an algorithm which finds binomials in a given ideal
$I\subset\mathbb{Q}[x_1,\dots,x_n]$ 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.
