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)*Reply-to*: drbob at bigfoot.com*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 bad: 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 > djmp at earthlink.net > http://home.earthlink.net/~djmp/