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Re: Re: Re: Collect exponents only

• To: mathgroup at smc.vnet.net
• Subject: [mg101488] Re: [mg101428] Re: Re: [mg101385] Collect exponents only
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 8 Jul 2009 07:13:27 -0400 (EDT)
• References: <200907070905.FAA22141@smc.vnet.net>

The FullForm of the expression on which Simplify is mapped looks  
like : Plus[u,v] where u is the (FullForm of) A*E^(I*(x + y) - I*x)  
and v the (FullForm of) A^2*E^(I*(x + y) - I*y). So by mapping  
Simplify on the expression we Simplify the summands without  
simplifying the sum itself. This is why no factorization takes place.

(Note that, in general
  f /@ g[a, b]
g[f[a], f[b]]
)

Andrzej

On 7 Jul 2009, at 18:05, Alexei Boulbitch wrote:

> Dear Andrzej,
>
> I realized that I cannot understand, how does one of the methods  
> that you give here work. It is the following:
>
> Simplify /@ (A*Exp[I*(x + y) - I*x] + A^2*Exp[I*(x + y) - I*y])
>
> A^2 E^(I x) + A E^(I y)
>
> On what elements do you map Simplify here? I would be grateful for  
> any explanation.
>
> Thank you, Alexei
>
>
>
> On 4 Jul 2009, at 19:43, Francisco Rojas wrote:
>
>> Hello,
>>
>> I was wondering if there's anyway to ask the command Simplify (or
>> maybe some other command) to only collect terms in the exponents of a
>> long expression (which contains complex exponentials by the way) and
>> not perform any other kind of simplification.
>>
>> For example I have an expression like this:
>>
>> A Exp[ I (x+y) - I x] + A^2 Exp[ I (x+y) - I y]           ( I is the
>> the imaginary unit )
>>
>> Mathematica does two simplications here: it simplifies the terms in
>> the exponents and factors out the A giving:
>>
>> A (Exp[ I y] + Exp[I x])
>>
>> whereas I would like to obtain only the exponents simplification,
>> i.e.   A^2 Exp[ I y] + A Exp[ I x]
>>
>> Anybody knows how to do this?
>> Thanks in advance,
>> Francisco
>>
>
>
> There is a vary large number of ways. For example:
>
> (A*Exp[I*(x + y) - I*x] + A^2*Exp[I*(x + y) - I*y]) /. Exp[p_] :>
> Exp[Simplify[p]]
> A^2 E^(I x) + A E^(I y
>
> or
>
> Expand[Simplify[A*Exp[I*(x + y) - I*x] + A^2*Exp[I*(x + y) - I*y]]]
> A^2*E^(I*x) + A*E^(I*y)
>
> or
>
> Simplify /@ (A*Exp[I*(x + y) - I*x] + A^2*Exp[I*(x + y) - I*y])
>
> A^2 E^(I x) + A E^(I y)
>
> or even
>
> Simplify[A*Exp[I*(x + y) - I*x] + A^2*Exp[I*(x + y) - I*y],
> ExcludedForms -> A^2]
> A^2*E^(I*x) + A*E^(I*y)
>
> Andrzej Kozlowski
>
>
> -- 
> Alexei Boulbitch, Dr., habil.
> Senior Scientist
>
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• References:
  • Re: Re: Collect exponents only
    • From: Alexei Boulbitch <Alexei.Boulbitch@iee.lu>