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

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

```

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