1In fact even if one realized from the beginning of the computation that a and c have no common eigenvalues, there is no way to express this hypothesis using polynomial equations. In fact, a complete analytic argument which showed that b = 0 would consist of an algebraic derivation of the identity ab = bc followed by the use of the hypothesis that a and c have no common eigenvalues. One would not in general know in advance that ab = bc and so it would be premature to add “b=0” to the collection of polynomial equations at the beginning of the computation.