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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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