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Re: Algebraic Manipulation



On 9 Feb 2004, at 11:54, 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,

Simplify[expr, r^2 == x^2 + y^2 + z^2]

(k*x*y)/(r^2*(k + r))

I suspect you did not try this because it was too obvious ;-)

Andrzej


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/


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