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Re: Replace each f in f^n to different variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126059] Re: Replace each f in f^n to different variables
  • From: Yi Wang <tririverwangyi at gmail.com>
  • Date: Sat, 14 Apr 2012 03:09:26 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <7BB0E96E72E84E41B24A1FF8ED13F5E629998E33CD@IE2RD2XVS581.red002.local>

Of course thank Ray as well! Sorry for this additional post but
interestingly Ray's reply didn't show up in my email and I cannot
modify my post.

On Fri, Apr 13, 2012 at 6:25 AM, Yi Wang <tririverwangyi at gmail.com> wrote:
> Thanks a lot, Bob and Alexei! Yes, those methods work very well.
>
> Best,
> Yi
>
> On Fri, Apr 13, 2012 at 3:18 AM, Alexei Boulbitch
> <Alexei.Boulbitch at iee.lu> wrote:
>> 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.
>>
>>
>> Hi, Yi,
>>
>> Is this:
>>
>> replaceFun[g_] := If[MatchQ[g, Power[_, _]],
>>   If[IntegerQ[g[[2]]],
>>
>>    Times @@ Table[ToExpression["var" <> ToString[i]], {i, 1, g[[2]]}],
>>         Print[
>>     Style["Error: the function \!\(\*SuperscriptBox[\(f\), \(n\)]\) \
>> has a non-integer exponent n", Red]]
>>       ],
>>   Print[Style[
>>     "Error: the function does not have the form \
>> \!\(\*SuperscriptBox[\(f\), \(n\)]\)", Red]]
>>   ];
>>
>>
>> replaceFun[f[x]^4.1]
>> replaceFun[Sin[x]^6]
>>
>> Error: the function f^n has a non-integer exponent n
>>
>> var1 var2 var3 var4 var5 var6
>>
>> what you are looking for?
>>
>> Have fun, Alexei
>>
>>
>> Alexei BOULBITCH, Dr., habil.
>> IEE S.A.
>> ZAE Weiergewan,
>> 11, rue Edmond Reuter,
>> L-5326 Contern, LUXEMBOURG
>>
>> Office phone :  +352-2454-2566
>> Office fax:       +352-2454-3566
>> mobile phone:  +49 151 52 40 66 44
>>
>> e-mail: alexei.boulbitch at iee.lu
>>
>>
>>
>>



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