How to Recognize Zero

An elementary point is a point in complexnspace, which is an isolated, nonsingular solution ofnequationsinnvariables, each equation being either of the formp = 0, wherepis a polynomial in Q [x1,…,xn], or of the formxj − exi = 0. An elementary number is the polynomial image of an elementary point. In this article a semi algorithm is given to decide whether or not a given elementary number is zero. It is proved that this semi algorithm is an algorithm, i.e. that it always terminates, unless it is given a problem containing a counterexample to Schanuel’s conjecture.