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I want to write a function via a module that takes a user's input and creates a function from the input within the module.

That is something like

Input:

G[nterm_] := 
  Module[{n, r},
    r[n_] := nterm
    r[n+1]]

G[n^2]

Output:

(n+1)^2

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    $\begingroup$ My math must be slipping: how did you get from $n^2$ to $(n+1)^2$? $\endgroup$ Commented Jun 9, 2016 at 5:17
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    $\begingroup$ It should return a function or just an expression like above? $\endgroup$
    – Kuba
    Commented Jun 9, 2016 at 6:32
  • $\begingroup$ Thanks for the quick response, please let me put in in context.. I'm implementing Gosper's algorithm (page 87 of A=B: math.upenn.edu/~wilf), so it needs to take a hypergeometric term as input and convert it to a rational function (or expression?) r(n) = t(n+1)/t(n) then execute a series of loops etc. The problems arise in the loops where the function definition is updated throughout. Simply defining a function f[n_]:=blah and trying to update it's definition in a loop doesn't seem to work. It seems replacement rules using /.-> might offer the solution.. not sure though? $\endgroup$
    – MathMuppt
    Commented Jun 10, 2016 at 1:43

1 Answer 1

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I don't see any reason to use Module for what you seem to asking. I suggest

g[expr_, var_Symbol] := If[FreeQ[expr, var], $Failed, expr /. var -> var + 1]

Then

g[n^2, n]

(1 + n)^2

g[2 Sqrt[x] + y^x, x]

2 Sqrt[1 + x] + y^(1 + x)

but

g[a + Sqr[x], y]

$Failed

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