Re: Simplifying complicated expressions

*To*: mathgroup at smc.vnet.net*Subject*: [mg110193] Re: Simplifying complicated expressions*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Mon, 7 Jun 2010 08:07:17 -0400 (EDT)

Make the LHS of the rule as simple as possible expr = Total[(x^2 + y^3 - x^2 y^2 + Sqrt[z3 + y2])^Range[-2, 2]]; While straight replacement isn't very effective expr /. (x^2 + y^3 - x^2 y^2 + Sqrt[z3 + y2]) -> f1xyz f1xyz + (-(x^2*y^2) + x^2 + y^3 + Sqrt[y2 + z3])^2 + 1/(-(x^2*y^2) + x^2 + y^3 + Sqrt[y2 + z3]) + 1/(-(x^2*y^2) + x^2 + y^3 + Sqrt[y2 + z3])^2 + 1 Using a simple LHS pattern that doesn't change in the various components of the FullForm representation works well repl = Sqrt[z3 + y2] -> f1xyz - (x^2 + y^3 - x^2 y^2); expr2 = expr /. repl f1xyz^2+1/f1xyz^2+f1xyz+1/f1xyz+1 val = {x -> 3, y -> 1, y2 -> 6, z3 -> 10}; repl2 = Solve[Equal @@ repl, f1xyz][[1]] /. val {f1xyz->5} expr2 /. repl2 781/25 % == (expr /. val) True Bob Hanlon ---- "S. B. Gray" <stevebg at ROADRUNNER.COM> wrote: ============= Suppose I have a long complex expression in which terms like (x^2+y^3-x^2y^2+Sqrt[z3+y2]) (for a simple example) appear many times along with various powers and the reciprocals of it, etc. To make the expression comprehensible and to make the computation faster, I would like to substitute say "f1xyz" for it everywhere it appears. The normal /. and -> substitutions and patterns are not adequate for this. Of course at evaluation time I want to compute f1xyz only once and not have the final formula revert to the original variables. How do I prevent that? Also a welcome addition to Mathematica would be the ability to find these repeated expressions automatically and put them in, because doing it manually is very error-prone and slow. Tips will be appreciated! Steve Gray