Re: Simplifying the exponents

• To: mathgroup at smc.vnet.net
• Subject: [mg80013] Re: Simplifying the exponents
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 10 Aug 2007 06:40:59 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f9gv3l\$b5e\$1@smc.vnet.net>

Jung-Tsung Shen wrote:
> Hello, I would like to ask a question which I haven't been able to
> find a solution that does not need human intervening.
>
> I would like to simplify the following expression
>
> Exp[I (q1 y1 + q2 y2 + q3 y3) - I (qp1 y1 + qp2 y2 + qp3 y3)]
>
> according to y1, y2, and y3 so it would look like
>
> Exp[I (q1-qp1) y1+ I (q2-qp2) y2 + I (q3-qp3) y3], or
>
> Exp[I (q1-qp1) y1] * Exp[I (q2-qp2) y2] * Exp[I (q3-qp3) y3]
>
> How could I achieve this in an efficient way?

Reorganize your exponent and then apply Collect w.r.t. y1, y2, and y3.

In[1]:=
expr = Exp[I*(q1*y1 + q2*y2 + q3*y3) - I*(qp1*y1 + qp2*y2 + qp3*y3)]
(Collect[Factor[#1], {y1, y2, y3}] & ) /@ expr
(Collect[Expand[#1], {y1, y2, y3}] & ) /@ expr

Out[1]=
I (q1 y1 + q2 y2 + q3 y3) - I (qp1 y1 + qp2 y2 + qp3 y3)
E

Out[2]=
I (q1 - qp1) y1 + I (q2 - qp2) y2 + I (q3 - qp3) y3
E

Out[3]=
(I q1 - I qp1) y1 + (I q2 - I qp2) y2 + (I q3 - I qp3) y3
E

--
Jean-Marc

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