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How to input an equation with implicit variables?

Posted 11 years ago
I want to input an equation, to be solved later in combination with many other equations, that reads f(q,t) == g(1/t, 1/q), where f and g are some functions of q and tt to be determined precisely by the other equations.  The problem is, I don't know how to input this equation: if I just use variables f and g and then write something like f/.{t->q, q->t} == g, then the replacement rule evaluates immediately and the equation to be solved becomes f==g, which is not what I want.  How should I input this equation into Mathematica?  Sorry if this question is obvious--I'm a Mathematica novice.
POSTED BY: Tom Rudelius
2 Replies
Copy of the question and a slightly longer thread in http://community.wolfram.com/groups/-/m/t/209858
POSTED BY: Bruce Miller
Hello
I believe this may be what you looking for?

Functions to be used later
exampleF1[u_, v_] := u Cos[v]
exampleF2[u_, v_] := ArcTan[u, v]
exampleG1[u_, v_] := (u + v) u
exampleG2[u_, v_] := (u - v) Exp[v]

Function to create your equation, and example usage
myEquation[f_, g_, q_, t_] := f[q, t] == g[1/t, 1/q]

myEquation[exampleF1, exampleG1, q, t]

myEquation[exampleF2, exampleG1, q, t]
POSTED BY: W. Craig Carter
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