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Re: Pattern Matching for Exponentials

• To: mathgroup at smc.vnet.net
• Subject: [mg67516] Re: Pattern Matching for Exponentials
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Thu, 29 Jun 2006 00:09:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 6/28/06 at 3:52 AM, reller at bigpond.com (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.

The problem is that

In[11]:=
MatchQ[2 I t, a_ I t]

Out[11]=
False

In[12]:=
MatchQ[2 I t, a_ t]

Out[12]=
True

So, you need

In[13]:=
Exp[2 I t]/.Exp[a_ t]->Exp[a t]/(Im[a]^2-1)

Out[13]=
(1/3)*E^(2*I*t)

but note if instead of Exp[2 I t] you had Exp[b I t] then

In[15]:=
Exp[b I t]/.Exp[a_ I t]->Exp[a I t]/(a^2-1)

Out[15]=
E^(I*b*t)/(b^2 - 1)

works fine
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