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Algebraic Manipulation

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

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))


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 

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