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 > > IEE S.A. > ZAE Weiergewan > 11, rue Edmond Reuter > L-5326 Contern > Luxembourg > > Phone: +352 2454 2566 > Fax: +352 2454 3566 > > Website: www.iee.lu > > This e-mail may contain trade secrets or privileged, undisclosed or > otherwise confidential information. If you are not the intended > recipient and have received this e-mail in error, you are hereby > notified that any review, copying or distribution of it is strictly > prohibited. Please inform us immediately and destroy the original > transmittal from your system. Thank you for your co-operation. > > >

**References**:**Re: Re: Collect exponents only***From:*Alexei Boulbitch <Alexei.Boulbitch@iee.lu>

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