Re: Solve[] for equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg31946] Re: [mg31928] Solve[] for equations?*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Thu, 13 Dec 2001 01:08:55 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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 evaluate: 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 JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ 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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