       Re: Algebraic Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg46182] Re: Algebraic Manipulation
• From: Dr Bob <drbob at bigfoot.com>
• Date: Tue, 10 Feb 2004 00:05:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Daniel Lichtblau recently had a post that used GroebnerBasis for a similar
purpose, and that method might be more powerful. But this problem's not

Clear[expr, x, y, z]
Solve[{expr ==
x*y*(-(1/(r*(k + r))) +
1/(x^2 + y^2) -
z^2/(r^2*(x^2 + y^2))),
r^2 == x^2 + y^2 + z^2},
expr, z]

{{expr -> (k*x*y)/
(r^2*(k + r))}}

Bobby

"David Park" <djmp at earthlink.net> wrote in message
news:<c07p9h\$kmc\$1 at smc.vnet.net>...
> 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