       Re: Algebraic Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg46188] Re: [mg46159] Algebraic Manipulation
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 10 Feb 2004 00:06:01 -0500 (EST)
• References: <200402091054.FAA20968@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```
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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