       Re: Algebraic Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg46233] Re: Algebraic Manipulation
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 12 Feb 2004 07:15:58 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <c07p9h\$kmc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Equal @@ Solve[Eliminate[
{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}, z], expr][[1, 1]]

Regards
Jens

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