Re: Common factors in a list

• To: mathgroup at smc.vnet.net
• Subject: [mg58348] Re: [mg58327] Common factors in a list
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Tue, 28 Jun 2005 21:56:46 -0400 (EDT)
• References: <200506280913.FAA05152@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 28 Jun 2005, at 18:13, 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
>

What you are asking for is impossible in Mathematica because
Mathematica automatically evaluates

a *{x, y, z}

{a x,a y,a z}

So you need to factor {a x, a y, a z} in some other form, for example
as {a,{x,y,z}}. This can be done as follows:

f[l_List] := With[{a = PolynomialGCD @@ l}, {a, Cancel[l/a]}]

for example

f[{x*BesselI[n, x]*BesselK[m, x], x*BesselI[n, x]*Exp[x]}]

{x*BesselI[n, x], {BesselK[m, x], E^x}}

Andrzej Kozlowski
Chiba, Japan

```

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