Re: Solve[] for equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg31941] Re: [mg31928] Solve[] for equations?*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Thu, 13 Dec 2001 01:08:47 -0500 (EST)*References*: <200112120914.EAA28804@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Are you sure there is a solution? I tried a system of two equations and here the solution doesn't exist: In[1]:= eq1 = Rac == R1*(R2/(R1 + R2)); eq2 = Rad == R2*(R1/(R1 + R2)); In[2]:= Timing[Solve[{eq1, eq2}, {R1, R2}]] Out[2]= {0.*Second, {}} Mathematica gives the right answer: there is no solution, as can be verified by hand. Either R1+R2 = 0, which leads to an indetermination in both equations, or Rac = Rad, which makes the system trivial. However, the three-equation system does have a solution: In[3]:= eq1 = Rac == R1*((R2 + R3)/(R1 + R2 + R3)); eq2 = Rad == R2*((R1 + R3)/(R1 + R2 + R3)); eq3 = Rbc == R3*((R1 + R2)/(R1 + R2 + R3)); In[4]:= Timing[Solve[{eq1, eq2, eq3}, {R1, R2, R3}]] Out[4]= {0.17 *Second, {{R1 -> (Rac^2 - 2*Rac*Rad + Rad^2 - 2*Rac*Rbc - 2*Rad*Rbc + Rbc^2)/(2*(Rac - Rad - Rbc)), R2 -> (-Rac^2 + 2*Rac*Rad - Rad^2 + 2*Rac*Rbc + 2*Rad*Rbc - Rbc^2)/(2*(Rac - Rad + Rbc)), R3 -> (-Rac^2 + 2*Rac*Rad - Rad^2 + 2*Rac*Rbc + 2*Rad*Rbc - Rbc^2)/(2*(Rac + Rad - Rbc))}}} You may verify the solution by direct substitution of these rules in the equations. Then, there is no solution for the 2-equation case, but there is a solution for the 3-equation case. I tried to set up a similar system with five equations, but it was taking too long to solve before I quit (over 30 minutes). I only wish to point out that there may actually not be a solution for the 4 equations (and, by the way, 4 equations in 4 unknowns doesn't mean anything unless they are linear equations). Tomas Garza Mexico City ----- Original Message ----- From: "Doug VanGoethem" <djvango at sandia.gov> To: mathgroup at smc.vnet.net Subject: [mg31941] [mg31928] Solve[] for equations? > 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 > > > > > >

**References**:**Solve[] for equations?***From:*"Doug VanGoethem" <djvango@sandia.gov>