  Let $I$ be an arbitrary ideal generated by binomials. We show that certain
equivalence classes of fibers are associated to any minimal binomial generating
set of $I$. We provide a simple and efficient algorithm to compute the
indispensable binomials of a binomial ideal from a given generating set of
binomials and an algorithm to detect whether a binomial ideal is generated by
indispensable binomials.

Commutative Algebra