  Binomial ideals are special polynomial ideals with many algorithmically and
theoretically nice properties. We discuss the problem of deciding if a given
polynomial ideal is binomial. While the methods are general, our main
motivation and source of examples is the simplification of steady state
equations of chemical reaction networks. For homogeneous ideals we give an
efficient, Gr\"obner-free algorithm for binomiality detection, based on linear
algebra only. On inhomogeneous input the algorithm can only give a sufficient
condition for binomiality. As a remedy we construct a heuristic toolbox that
can lead to simplifications even if the given ideal is not binomial.
