Simplification is a central and basic operation in the manipulation of mathematical expressions. Indeed, much of the tedious algebra that plagues scientists and engineers involves the time-consuming application of simplifying transformations to unwieldly mathematical expressions. It seems obvious, conceptually, that some simplifying transformations can be applied automatically to arbitrary expressions. However, there are transformations that require special handling; they simplify some expressions and complicate others.
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Tobey et al. (1965) studied this question.
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