Re: Replace each f in f^n to different variables
- To: mathgroup at smc.vnet.net
- Subject: [mg126049] Re: Replace each f in f^n to different variables
- From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
- Date: Fri, 13 Apr 2012 04:57:52 -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.
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,
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L-5326 Contern, LUXEMBOURG
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e-mail: alexei.boulbitch at iee.lu