Algebraic re-substitution

*To*: mathgroup at smc.vnet.net*Subject*: [mg70946] Algebraic re-substitution*From*: "James" <cannonjunk at hotmail.com>*Date*: Thu, 2 Nov 2006 06:48:09 -0500 (EST)

Hello, I am trying to work out how to simplify an equation by resubstituting variables back into the result to make the result more readable. As a simple example: In three dimentions, the distance between two points is given by: r[xi_,yi_,zi_,xj_,yj_zj_] := Sqrt[(xj-xi)^2 + (yj-yi)^2 + (zj-zi)^2] If I have an equation like: V=r[xi,yi,zi,xj,yj,zj]^2+2r[xi,yi,zi,xj,yj,zj]-5 Then I can tell mathematica to find the derivative, wrt xi: f=D[V,xi] This will then result in a long equation with many xi's, yi's, etc... which would look much cleaner and simpler is mathematica re-substituted r back into the equation. How can I get mathematica to do this? I have been playing with Simplify and FullSimplify, but I can't work it out. My actual problem is much more complicated, but I made this up as a basic example to illustrate the question. Any assistance would be greatly appreciated! Thanks! James in Japan