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Re: Pattern Matching for Exponentials

• To: mathgroup at smc.vnet.net
• Subject: [mg67503] Re: Pattern Matching for Exponentials
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 29 Jun 2006 00:08:59 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <e7tejf$444$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.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.
> 
> Thanks,
> 
> Rick Eller
> 
Hi Rick,

Well, I do not know what to say since that works fine on my system:

In[1]:=
Exp[2*i*t]

Out[1]=
  2 i t
E

In[2]:=
FullForm[%]

Out[2]//FullForm=
Power[E, Times[2, i, t]]

In[3]:=
MatchQ[Exp[2*i*t], Exp[(n_)*i*t]]

Out[3]=
True

In[4]:=
Exp[2*i*t] /. Exp[(n_)*i*t] -> 0

Out[4]=
0

In[5]:=
Exp[2*i*t] /. Exp[(n_)*i*t] -> Exp[n*i*t]/(n^(2) - 1)

Out[5]=
1  2 i t
- E
3

In[6]:=
$Version

Out[6]=
5.2 for Microsoft Windows (June 20, 2005)

HTH,
Jean-Marc