 ISSAC 94 - Symbolic-Numeric Nonlinear Equation Solving Contents News View

 Elementary Solutions  Bundy and Welham 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

(1) (2)  (3) (4)  (5) (6) (7) (8) where and is an integer-valued 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.       ©2004-2021 Planet Quantum Kelly Roach