MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: equation is too complex?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22557] Re: [mg22473] equation is too complex?
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sat, 11 Mar 2000 17:52:34 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

on 3/8/00 8:22 AM, heg7 at cornell.edu at heg7 at cornell.edu wrote:

> 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
> 
> 


I have had a quick look at your equation and it seems to me that the problem
is not simply that it is too complex for Mathematica but rather that it
actually lacks a well defined mathematical meaning. You seem to believe that
there should exist a formula which expresses ld in terms of the other
"variables" but actually it is not at all clear if such an object is well
defined. The problem is: what sort of mathematical object would a solution
to this equation be? It would have to be an element of some field but which
field? Even if we take the largest field in which this equation makes sense,
i.e. the algebraic closure of the transcendental extension of the complex
numbers by indeterminates corresponding to your parameters, there is no
reason to expect that you should be able to write solutions in terms of
"radicals", and even if you could make sense of that I do not think there is
any algorithm that could be used to find such solutions.

It seems to me that these sort of problems are simply not mathematically
well defined, except in very simple cases.


-- 
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp




  • Prev by Date: Re: export graphic to ps---trouble with fonts
  • Next by Date: Re: ScatterPlot3D with vertical lines
  • Previous by thread: equation is too complex?
  • Next by thread: Defining a function within a module