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Re: Solve[] for equations?

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  • Subject: [mg31946] Re: [mg31928] Solve[] for equations?
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Thu, 13 Dec 2001 01:08:55 -0500 (EST)
  • Sender: owner-wri-mathgroup at

The concept may be simple but the practice is not quite so. You can see 
that as follows.
Here are your equations.

eq1 = Rac == R1(R2 + R3 + R4)/(R1 + R2 + R3 + R4)
eq2 = Rad == R2(R1 + R3 + R4)/(R1 + R2 + R3 + R4)
eq3 = Rbc == R3(R1 + R2 + R4)/(R1 + R2 + R3 + R4)
eq4 = Rbd == R4(R1 + R2 + R3)/(R1 + R2 + R3 + R4)

we ask Mathematica to eliminate all the variables except one (say R4).

eq5 = Eliminate[{eq1, eq2, eq3, eq4}, {R1, R2, R3}];

You have to wait a bit for this to work (Mathematica 4.1).

If you want to see the 4th degree equation in R4 that you get you can 

eq5 /. Equal[x_, y_] :> Collect[x - y, R4] == 0

What you see is a fourth degree equation with symbolic coefficients 
which is far from simple. Mathematica can actually "solve" it with:

Solve[eq5, R4]

You have to wait quite a while and then you will see something 
phenomenally complicated and in my opinion essentially useless (and in 
addition there is basically no way of checking its correctness).

If you like that you can use the same approach to get R1,R2 and R3 or 
much  better, you can just use the symmetry of your equations to find 
out the other answers (to get R3 just replace Rbd by Rbc and vice versa).

Andrzej Kozlowski
Toyama International University

On Wednesday, December 12, 2001, at 06:14  PM, Doug VanGoethem wrote:

> I have a system of equations
> eq1 = Rac == R1(R2+R3+R4)/(R1+R2+R3+R4)
> eq2 = Rad == R2(R1+R3+R4)/(R1+R2+R3+R4)
> eq3 = Rbc == R3(R1+R2+R4)/(R1+R2+R3+R4)
> eq4 = Rbd == R4(R1+R2+R3)/(R1+R2+R3+R4)
> I'd like to get R1, R2, R3, and R4 in terms of Rac, Rad, Rbc, and Rbd.  
> Four
> equations, four unknowns -- it seems simple in concept so I figured 
> Mathematica
> could do it easily.  I thought that something along the lines of:
> Solve[{eqs},{R1, R2, R3, R4}] or
> Solve[{eqs}, R1, {R2, R3, R4}]
> would have worked, but these give {}.  They only permutation of commands
> that seemed to do anything was something like
> Solve[eq1, R1]
> but one can do that easily by hand so what's the point.
> Is there some other command I should be using besides Solve?   Is there 
> some
> mathematical reason that I don't recognize as to why this won't 
> work?   I
> would appreciate any insights.
> Thanks in advance,
> Doug VanGoethem

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