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MathGroup Archive 2004

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Re: Algebraic Manipulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46233] Re: Algebraic Manipulation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 12 Feb 2004 07:15:58 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <c07p9h$kmc$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Equal @@ Solve[Eliminate[
        {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}, z], expr][[1, 1]]

Regards
  Jens

David Park wrote:
> 
> Dear MathGroup,
> 
> 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?
> 
> (The problem arose in calculating the components of the Schwarzschild metric in Cartesian coordinates.)
> 
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/


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