Abstract
This paper uses elementary algebraic methods to obtain new proofs for theorems on algebraic relationships between the logarithmic and exponential functions. The main result is a multivariate version of a special case of the structure theorem due to Risch that gives, in a very explicit fashion, the possible algebraic relationships between the exponential and logarithm functions. The structure theorem has important applications to symbolic mathematical computation in that it in essence provides a canonical form for the elementary transcendental functions, and hence solves the identity problem for this class of functions. Such applications are discussed in the last section.
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This research was supported in part by National Science Foundation Grants GJ-30125X and MCS76-23762.
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Epstein, H.I., Caviness, B.F. A structure theorem for the elementary functions and its application to the identity problem. International Journal of Computer and Information Sciences 8, 9–37 (1979). https://doi.org/10.1007/BF00995426
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DOI: https://doi.org/10.1007/BF00995426