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Re: Collect exponents only

• To: mathgroup at smc.vnet.net
• Subject: [mg101407] Re: [mg101385] Collect exponents only
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 5 Jul 2009 04:48:08 -0400 (EDT)
• References: <200907041043.GAA17784@smc.vnet.net>

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

• References:
  • Collect exponents only
    • From: Francisco Rojas <fjrojas@gmail.com>