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equation is too complex?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22473] equation is too complex?
  • From: heg7 at cornell.edu
  • Date: Wed, 8 Mar 2000 02:22:11 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I am having problems solving equations in Mathematica.
There are two approaches I have tried:
1. I have a system of five equations (involving 
Cobb-Douglas forms)in five variables. When I use the 
"Solve" command, I get the empty solution set {}. When I 
use "Reduce," Mathematica runs for a long time. I have 
let it run for about 15 minutes before interrupting the 
calculations.
2. I have reduced these equations by hand into 1 
equation in 1 variable. The resulting equation is quite 
ugly, with a number of long expressions raised to 
exponents between -1 and 1 (see below for the equation). 
When I use "Solve," Mathematica gives me back the 
equation in a slightly simplified form as output. When I 
use "Reduce," Mathematica again seems to take a long 
time.

My questions are the following:
Might I be doing something wrong?
Are these equations too complex for Mathematica to 
solve? If not, how much time should Mathematica take to 
solve these problems?
Is there something I can do to speed up the process?

Thank you very much.

Heidi Gjertsen

The equation: (I'm solving for ld)

(-1/4)*(6*w-ld*w/4+(1/ld+y^(1/2)*z^(1/2))*ld/4*y)^(1/2)*
(
          
12-ld/2+(1/ld+y^(1/2)*z^(1/2))^(1/2)*ld/2*y*w)^(-3/4)*(
          1/ld+y^(1/2)*z^(1/2))^(1/4)+(
        
1/4)*(6*w-ld*w/4+(1/ld+y^(1/2)*z^(1/2))*ld/4*y)^(1/2)*(
          
12-ld/2+(1/ld+y^(1/2)*z^(1/2))^(1/2)*ld/2*y*w)^(-1/4)*(
          1/ld+y^(1/2)*z^(1/2))^(-3/4)*(-1/(ld^2))+(
          
6*w-ld*w/4+(1/ld+y^(1/2)*z^(1/2))*ld/4*y)^(-1/2)*(
          
12-ld/2+(1/ld+y^(1/2)*z^(1/2))^(1/2)*ld/2*y*w)^(1/4)*(
          1/ld+y^(1/2)*z^(1/2))^(
          
1/4)*((1/ld+y^(1/2)*z^(1/2))^(-1/2)*(-1/((ld^2)*24))+(
                1/ld+y^(1/2)*z^(1/2))^(1/2)*(1/y)) == 0


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