       Re: Factoring

• To: mathgroup at smc.vnet.net
• Subject: [mg65146] Re: Factoring
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 15 Mar 2006 06:30:41 -0500 (EST)
• Organization: The University of Western Australia
• References: <dv6847\$nq4\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <dv6847\$nq4\$1 at smc.vnet.net>,
"Matt" <anonmous69 at netscape.net> wrote:

> Hello Mathgroup,
>   I'm sure that I've overlooked something obvious, but for the past two
> and a half hours, I've been trying to figure out how to use built-in
> Mathematica functions to just factor the imaginary number 'I' out of
> this:
>
> 4*I*r^2*Sin[2*Î¸] + I*r^5*Sin[5*Î¸]
>
> using Factor[] gives me I*r^2*(4*Sin[2*Î¸] + r^3*Sin[5*Î¸])
>
> using FactorTerms[] gives me I*(4*r^2*Sin[2*Î¸] + r^5*Sin[5*Î¸]) which
> is what I want, but as soon as I add in a common numerical factor, it
> also factors that out as well,
>
> e.g. 4*I*r^2*Sin[2*Î¸] + 8*I*r^5*Sin[5*Î¸]

ComplexExpand does what you want:

ComplexExpand[I Sin[5 x] r^5 + 4 I Sin[2 x] r^2]

Note that FullForm can be very useful in understanding what is required
here. For example,

FullForm[ 4 I ]

is _not_ Times[4, Complex[0,1]].

> As an additional example, what
> if I just wanted to extract 2*x*I out of the following:
>
> 4*x*I*Sin[t] + 28*x^3*I*Cos[t]
>
> how would I do that?  In general, I'm looking for a function that says
> "Given an expression 'expr' and another expression 'sub' that is common
> to all additive terms of 'expr', give a result that is the product of
> 'sub' and the result of factoring 'sub' out of 'expr'".

Well, you've described exactly the procedure for doing this. Essentially
"divide" 'expr' by 'sub' and then back multiply:

FactorOut[expr_, sub_, var_]:= sub PolynomialQuotient[expr, sub, var] /;
PolynomialQ[expr, var] && PolynomialQ[sub, var]

FactorOut[28 I Cos[t] x^3 + 4 I Sin[t] x, 2 x I, x]

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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