
Bundy and Welham[3] describe concepts of attraction, collection, and isolation which sometimes lead to solutions of nonlinear equations. Taking a somewhat related algorithmic approach, suppose is an elementary expression where each is exponential, logarithmic, or algebraic. Factoring, we suppose is irreducible in . Apply rules
where and is an integervalued piecewise constant function of . For rule (1), let and be exponentials. Try to find integers , , such that (consider and degrees) and simplify to where . For rule (2), let and be logarithms. Try to find a rational such that (consider , , and lcoeff's) and simplify to where , , and is chosen according to a given root (given by our numerical algorithm). Rules (1)(2) are applied first. Rules (3)(8) are applied with new factorization. This scheme will solve some equations. 

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