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MathGroup Archive 2004

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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
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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