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Re: Algebraic Manipulation


Hi David,

I have got to your results using FullSimplify with assumptions:

expr = x*y*(-(z^2/(r^2*(x^2 + y^2))) - 1/(r*(k + r)) + 1/(x^2 + y^2));

FullSimplify[expr, {r >= 0, r^2 == x^2 + y^2 + z^2}]

Best,
Sasha

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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