Zero Tests for Constants in Simple Scientific Computation

Abstract.

It would be desirable to have an algorithm to decide equality among the constants which commonly occur in scientific computing. We do not yet know whether or not this is possible. It is known, however, that if the Schanuel conjecture is true, then equality is Turing decidable among the closed form numbers, that is, the complex numbers built up from the rationals using field operations, radicals, exponentials and logarithms. An algorithm based on the Schanuel conjecture is described in this article to decide equality among these numbers, presented as expressions. The algebraic part of this algorithm is simpler than those which have been given previously to solve related problems.