Automatic numerical expansions


Let exp-log constants be those real numbers which are built up from the rationals, by field operations, exponentiation and logarithm. Theoretically, the sign of an exp-log constant can be determined by floating point computations, whenever we can decide whether the constant is zero or not. However, this method has a complexity which is worse than any iterated exponential, even in concrete cases. We propose an algorithm, combining floating point evaluations with asymptotic methods, which is expected to be efficient in practice.

Keywords: numerical expansion, exp-log constant, floating point evaluation, asymptotics, algorithm

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