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Re: Common factors in a list
*To*: mathgroup at smc.vnet.net
*Subject*: [mg58366] Re: Common factors in a list
*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>
*Date*: Tue, 28 Jun 2005 21:56:59 -0400 (EDT)
*References*: <d9r50q$568$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
John Reed wrote:
> I'm working with a list (vector) that's composed of functions such as
> complex exponentials and Bessel functions. Some of the functions are common
> to each element of the list. I'm trying to find a way to do the following:
>
> {a x, a y, a z}-> a *{x, y, z}
>
> In this expression, a, x, y, z are polynomials, exponentials and/or Bessel
> functions.
>
> So far I haven't had any luck with this. Does anyone have a simple
> solution?
>
> John Reed
>
Hello,
The best bet is to make use of Factor. This seems rather more powerful
than the help might suggest - for example it recognises that Exp[a+b] is
Exp[a]Exp[b]. To use Factor, convert the list into a polynomial in an
otherwise unused variable - say q:
Plus@@MapIndexed[#1 q^(#2[[1]]-1)&,{a Exp[m],b Exp[m+n], c Exp[m]}]
a*E^m + b*E^(m + n)*q + c*E^m*q^2
Factor[%]
E^m*(a + b*E^n*q + c*q^2)
It is not possible to convert the result back into a product of a term
and a list (as you specified) because this will evaluate and leave you
where you began! Instead, we can replace the product with a CircleTimes:
E^m*(a + b*E^n*q + c*q^2) /. (p1_)*(p2_Plus) :> p1 \[CircleTimes]
CoefficientList[p2, q]
E^m \[CircleTimes] {a, b*E^n, c}
David Bailey
http://www.dbaileyconsultancy.co.uk
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