RE: Algebraic re-substitution
- To: mathgroup at smc.vnet.net
- Subject: [mg70964] RE: [mg70946] Algebraic re-substitution
- From: "David Park" <djmp at earthlink.net>
- Date: Fri, 3 Nov 2006 01:39:10 -0500 (EST)
James, Simple, define a rule to reverse substitute. r[xi_, yi_, zi_, xj_, yj_, zj_] := Sqrt[(xj - xi)^2 + (yj - yi)^2 + (zj - zi)^2] rrule = r[xi, yi, zi, xj, yj, zj]^2 -> r^2; V = r[xi, yi, zi, xj, yj, zj]^2 + 2r[xi, yi, zi, xj, yj, zj] - 5; f = D[V, xi]; Simplify[% /. rrule, r > 0] (2*(1 + r)*(xi - xj))/r David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: James [mailto:cannonjunk at hotmail.com] To: mathgroup at smc.vnet.net 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