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Re: Adding new rules to Simplify


Here's another one!

r1[x_ /; ! FreeQ[x, f]] := x /. f[y_] -> a[y]/b[y]; 
r1[x_] := x;

r2[x_ /; ! FreeQ[x, g]] := x /. g[y_] -> b[y]/a[y]; 
r2[x_] := x;

Simplify[f[X] g[X], TransformationFunctions -> {r1, r2}]

gives 

f(X) g(X)


I would have hoped to get 1 here, particularly since

r1[r2[f[X]g[X]]]

gives me 1 as expected! 

So I tell it to Simplify using just two rules, the successive application of which gives 1, but Mathematica fails to simplify at all.

What's going on here??

John


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