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This paper describes a procedure for determining when a set of rational functions are pseudo-multiplicatively independent, i.e. when no non-trivial power product of the rational functions can be a constant. The method used is to derive a multiplicative basis of factors of the numerators and denominators of the rational functions; the basis is then used to… (More)

It is a well-known empirical result that differentiation, especially higher order differentiation, of simple expressions can lead to long and complex expressions. In this paper we give some theoretical results that help to explain this phenomenon. In particular we show that in certain representations there exist expressions whose representations require… (More)

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