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Heuristics based on transcendentality

This is a useful heuristic, quite effective, but not widely applicable. The idea is best illustrated with an example. Suppose that our expression to match is a rational polynomial in x. Suppose that the pattern has terms in x and in ex. Since we know that no polynomial in x is equal to any polynomial in ex, then then only possible matching is one which eliminates all appearances of ex in the pattern.

Gaston Gonnet