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>*Reply-to*: kuska at informatik.uni-leipzig.de*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 > djmp at earthlink.net > http://home.earthlink.net/~djmp/