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Re: Simplifying the exponents

On 10 Aug 2007, at 07:50, 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?
> Thanks.
> JT

  (Collect[#1, {y1, y2, y3}] & ) /@ (E^(I*(q1*y1 + q2*y2 + q3*y3) - I* 
(qp1*y1 + qp2*y2 + qp3*y3)))

  E^((I*q1 - I*qp1)*y1 + (I*q2 - I*qp2)*y2 + (I*q3 - I*qp3)*y3)

Your second request is impossible in Mathematica (without using  
HoldForm), since Mathematica always evaluates

E^(a + b)

so even if you execute code that returns your desired output, this  
output (unless wrapped in HoldForm) will automatically be converted  
into the form above.

Andrzej Kozlowski

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