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Replace each f in f^n to different variables

• To: mathgroup at smc.vnet.net
• Subject: [mg125995] Replace each f in f^n to different variables
• From: Yi Wang <tririverwangyi at gmail.com>
• Date: Thu, 12 Apr 2012 02:33:19 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi, all,

I want to replace *each* f in f^n to a different variable, say

f^n -> var1 * var2 * ... * varn

Naively, if I try 

f^n /. f:>Unique[],

Mathematica simply returns (a unique variable)^n, instead of the above behaviour.

Is there a simple way to get the f's into different variables?

Thanks!
Yi

PS:

(1) I know there are ways to transform Power to a list by hand, and then do something in it. For example,

Times[((f^3)[[1]]*Table[1, {(f^3)[[2]]}]) /. f :> Unique[]]

However, eventually I will be dealing with a large expression, with all kinds of terms, instead of a single term. This method quickly becomes very complicated.

(2) I want to do such "strange" things, because a product of functions in position space f(x)^n becomes F(k1)F(k2)...F(k_{n-1})F(-k1-k2...) in momentum space.

• Follow-Ups:
  • Re: Replace each f in f^n to different variables
    • From: Bob Hanlon <hanlonr357@gmail.com>