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

**References**:**Simplifying the exponents***From:*"Jung-Tsung Shen" <jushen@gmail.com>