Re: Simplifying the exponents

• To: mathgroup at smc.vnet.net
• Subject: [mg80024] Re: [mg79994] Simplifying the exponents
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 10 Aug 2007 06:46:53 -0400 (EDT)
• References: <200708100550.BAA10857@smc.vnet.net>

```
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

Exp[a]*Exp[b]
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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