       Re: Pattern Matching for Exponentials

• To: mathgroup at smc.vnet.net
• Subject: [mg67505] Re: [mg67502] Pattern Matching for Exponentials
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 29 Jun 2006 00:09:02 -0400 (EDT)
• References: <200606280752.DAA03521@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 28 Jun 2006, at 16:52, Rick Eller wrote:

>
> I am looking for a pattern-matching replacement rule which will
> transform exponential functions of the form exp(n i t) into
> (1/(n^2-1))exp(n i t) where i = sqrt[-1]. For example, exp(2 i t)
> should convert to (1/3)exp(2 i t). I've tried the following code
> without
> success :
>
> In:     Exp[2 i t]   /.  Exp[n_ i t] -> Exp[n i t]/(n^2-1)
>
> Out:  e^2 i t
>
> I would appreciate any suggestions as to how this code should be
> modified.
>
> Thanks,
>
> Rick Eller
>

First of all, in Mathematica Sqrt[-1] can be input as I (capital
letter) or as \[ImaginaryI] but never as i. As for your question, you
should look at the FullForm of the expression you are trying to match
and the FullForm of the pattern you are using and you will see why
there is no Match. Here are a couple of possible solutions:

Unevaluated[Exp[2*I*t]] /. HoldPattern[Exp[(n_)*I*t]] ->
Exp[n*I*t]/(n^2 - 1)

(1/3)*E^(2*I*t)

Exp[2*I*t] /. HoldPattern[E^((Complex[0, n_])*t)] ->
Exp[n*I*t]/(n^2 - 1)

(1/3)*E^(2*I*t)

Andrzej Kozlowski
Tokyo, Japan

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