Re: Algebraic Manipulation
- To: mathgroup at smc.vnet.net
- Subject: [mg46226] Re: Algebraic Manipulation
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 12 Feb 2004 07:15:52 -0500 (EST)
- Organization: The University of Western Australia
- References: <c07p9h$kmc$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <c07p9h$kmc$1 at smc.vnet.net>,
"David Park" <djmp at earthlink.net> wrote:
> I'm always interested in Mathematica techniques for manipulating and
> simplifying algebraic expressions. I came across the following problem, which
> I was only able to do with a fair amount of difficulty.
>
> expr = x*y*(-(z^2/(r^2*(x^2 + y^2))) - 1/(r*(k + r)) + 1/(x^2 + y^2))
>
> where
>
> r^2 == x^2 + y^2 + z^2
>
> reduces to
>
> (k*x*y)/(r^2*(k + r))
>
> I wonder if anyone can show an elegant or short method to do the
> simplification?
How about
Clear[expr];
Solve[{expr==x y (-(z^2/(r^2 (x^2 + y^2)))-1/(r (k + r))+1/(x^2+y^2)),
r^2 == x^2 + y^2 + z^2, k != 0}, expr, z]
If k == 0 then expr reduces to 0.
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
School of Physics, M013 Fax: +61 8 9380 1014
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