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RE: Pattern Matching for Exponentials

• To: mathgroup at smc.vnet.net
• Subject: [mg67524] RE: [mg67502] Pattern Matching for Exponentials
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 29 Jun 2006 00:10:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Rick,

If you examine the FullForm of the expression and the pattern, you will see
that they do not match. (I'm using the actual Mathematica I for Sqrt[-1].)

Exp[2 I t] // FullForm
Power[E, Times[Complex[0, 2], t]]

Exp[n_ I t] // FullForm
Power[E, Times[Complex[0, 1], t, Pattern[n, Blank[]]]]

The following rule will match.

Exp[2 I t]   /.  Exp[Complex[0, n_] t] :> Exp[n I t]/(n^2 - 1)
(1/3)*E^(2*I*t)

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/



From: Rick Eller [mailto:reller at bigpond.com]
To: mathgroup at smc.vnet.net


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