Re: Algebraic Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg46175] Re: [mg46159] Algebraic Manipulation
• From: Oleksandr Pavlyk <pavlyk at phys.psu.edu>
• Date: Tue, 10 Feb 2004 00:05:42 -0500 (EST)
• Organization: Penn State University; Department of Physics
• References: <200402091054.FAA20968@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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
>

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