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Algebraic Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg46159] Algebraic Manipulation
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 9 Feb 2004 05:54:06 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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/ 

• Follow-Ups:
  • Re: Algebraic Manipulation
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Algebraic Manipulation
    • From: Oleksandr Pavlyk <pavlyk@phys.psu.edu>
  • Re: Algebraic Manipulation
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>