Re: Algebraic Manipulation

*To*: mathgroup at smc.vnet.net*Subject*: [mg46226] Re: Algebraic Manipulation*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Thu, 12 Feb 2004 07:15:52 -0500 (EST)*Organization*: The University of Western Australia*References*: <c07p9h$kmc$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <c07p9h$kmc$1 at smc.vnet.net>, "David Park" <djmp at earthlink.net> wrote: > 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? How about Clear[expr]; Solve[{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, k != 0}, expr, z] If k == 0 then expr reduces to 0. Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul