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Re: Algebraic Manipulation


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/





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