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>*Reply-to*: pavlyk at phys.psu.edu*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 > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > -- Office: 6H Osmond Web: http://www.pavlyk.com ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ No trees were destroyed to send this mail, but a lot of electrons were terribly disturbed.

**References**:**Algebraic Manipulation***From:*"David Park" <djmp@earthlink.net>