  Motivated by problems from Chemical Reaction Network Theory, we investigate
whether steady state ideals of reversible reaction networks are generated by
binomials. We take an algebraic approach considering, besides concentrations of
species, also rate constants as indeterminates. This leads us to the concept of
unconditional binomiality, meaning binomiality for all values of the rate
constants. This concept is different from conditional binomiality that applies
when rate constant values or relations among rate constants are given. We start
by representing the generators of a steady state ideal as sums of binomials,
which yields a corresponding coefficient matrix. On these grounds we propose an
efficient algorithm for detecting unconditional binomiality. That algorithm
uses exclusively elementary column and row operations on the coefficient
matrix. We prove asymptotic worst case upper bounds on the time complexity of
our algorithm. Furthermore, we experimentally compare its performance with
other existing methods.
