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MathGroup Archive 2007

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Re: Enquirey

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74823] Re: Enquirey
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 6 Apr 2007 04:26:21 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <ev2anc$k85$1@smc.vnet.net>

Rita Ray wrote:
> I am trying to solve two equation with two unknowns. I am using
> Mathematica 5.2.  Below is my program
> 
> 
> Solve[{a*Exp[2*w]-a^2*Exp[w+(x-y)*z]+a^2*Exp[w-(x-y)*z]-a*Exp[w+(x-y)*z]-a*=
> Exp[w-(x-y)*z]+a^2*Exp[2*(x-y)]+a-a^2+a^2*x*Exp[w+(x-y)*z]
> +a^2*x*Exp[w-(x-y)*z]-a*x*Exp[w+(x-y)*z]-a*x*Exp[w-(x-y)*z]+2*a*x-2*a^2*x-(=
> (a^3*w*Exp[w+(x-y)*z])/z)-((a^3*w*Exp[w-(x-y)*z])/z)+((a^2*w*Exp[w+(x-y)*z]=
> )/z)+((a^2*w*Exp[w-(x-y)*z])/z)-((2*a^2*w)/z)+((2*a^3*w)/z)====0,-((a*Exp[-=
> w+(x-y)*z]*z*(-((1-a)*w)-2*w*a^2+2*w*a^3+a^2*w*Exp[w-(x-y)*z]-a^3*w*Exp[w-(=
> x-y)*z]+a^2*w*Exp[w+(x-y)*z]-a^3*w*Exp[w+(x-y)*z]+a*z-a^2*z+a*z*Exp[2*w]+a^=
> 2*z*Exp[2*(x-y)]-a*z*Exp[w-(x-y)*z]+a^2*z*Exp[w-(x-y)*z]-a*z*Exp[w+(x-y)*z]=
> -a^2*z*Exp[w+(x-y)*z]+2*a*x*z-2*a^2*x*z-a*x*z*Exp[w-(x-y)*z]+a^2*x*z*Exp[w-=
> (x-y)*z]-a*x*z*Exp[w+(x-y)*z]+a^2*x*z*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(=
> 1-a)*Exp[-w-(x-y)*z]))-(a*Exp[-w+(x-y)*z]*((1-a)*z*Exp[-w-(x-y)*z]-a*z*Exp[=
> -w+(x-y)*z])*(-((1-a)*w)-2*w*a^2+2*w*a^3+a^2*w*Exp[w-(x-y)*z]-a^3*w*Exp[w-(=
> x-y)*z]+a^2*w*Exp[w+(x-y)*z]-a^3*w*Exp[w+(x-y)*z]+a*z-a^2*z+a*z*Exp[2*w]+a^=
> 2*z*Exp[2*(x-y)]-a*z*Exp[w-(x-y)*z]+a^2*z*Exp[w-(x-y)*z]-a*z*Exp[w+(x-y)*z]=
> -a^2*z*Exp[w+(x-y)*z]+2*a*x*z-2*a^2*x*z-a*x*z*Exp[w-(x-y)*z]+a^2*x*z*Exp[w-=
> (x-y)*z]-a*x*z*Exp[w+(x-y)*z]+a^2*x*z*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(=
> 1-a)*Exp[-w-(x-y)*z])^2+(a*Exp[-w+(x-y)*z]*(-2*a^2*z*Exp[2*(x-y)]+a^2*w*z*E=
> xp[w-(x-y)*z]-a^3*w*z*Exp[w-(x-y)*z]-a^2*w*z*Exp[w+(x-y)*z]+a^3*w*z*Exp[w+(=
> x-y)*z]-a*z^2*Exp[w-(x-y)*z]+a^2*z^2*Exp[w-(x-y)*z]+a*z^2*Exp[w+(x-y)*z]+a^=
> 2*z^2*Exp[w+(x-y)*z]-a*x*z^2*Exp[w-(x-y)*z]+a^2*x*z^2*Exp[w-(x-y)*z]
> +a*x*z^2*Exp[w+(x-y)*z]-a^2*x*z^2*Exp[w+(x-y)*z]))/(a*Exp[-w+(x-y)*z]+(1-a)=
> *Exp[-w-(x-y)*z])====0},{x,y}]
> 
> 
> Thank you.
> 
> Rita Ray.
> 
> Ph.D. student
> 

Four equal signs in a row (i.e. ====) does not mean anything in 
Mathematica. To set up an equation, what you want to use is two equal 
signs in a row (i.e. ==).

Since "Solve deals primarily with linear and polynomial equations 
(Online Help)," and Reduce returns the expression unevaluated with the 
message, "Reduce::nsmet: This system cannot be solved with the methods 
available to Reduce, you might want to try a different approach, like a 
numerical solution with NSolve.

eqn1 = (-a)*Exp[2*w] - a^2*Exp[w + (x - y)*z] +
  a^2*Exp[w - (x - y)*z] - a*Exp[w + (x - y)*z] -
  a*Exp[w - (x - y)*z] + a^2*Exp[2*(x - y)] + a -
  a^2 + a^2*x*Exp[w + (x - y)*z] +
  a^2*x*Exp[w - (x - y)*z] -
  a*x*Exp[w + (x - y)*z] - a*x*Exp[w - (x - y)*z] +
  2*a*x - 2*a^2*x - (a^3*w*Exp[w + (x - y)*z])/z -
  (a^3*w*Exp[w - (x - y)*z])/z +
  (a^2*w*Exp[w + (x - y)*z])/z +
  (a^2*w*Exp[w - (x - y)*z])/z - (2*a^2*w)/z +
  (2*a^3*w)/z == 0;

eqn2 = -((a*Exp[-w + (x - y)*z]*z*(-((1 - a)*w) -
  2*w*a^2 + 2*w*a^3 + a^2*w*
  Exp[w - (x - y)*z] - a^3*w*
  Exp[w - (x - y)*z] + a^2*w*
  Exp[w + (x - y)*z] - a^3*w*
  Exp[w + (x - y)*z] + a*z - a^2*z +
  a*z*Exp[2*w] + a^2*z*Exp[2*(x - y)] -
  a*z*Exp[w - (x - y)*z] +
  a^2*z*Exp[w - (x - y)*z] -
  a*z*Exp[w + (x - y)*z] -
  a^2*z*Exp[w + (x - y)*z] + 2*a*x*z -
  2*a^2*x*z - a*x*z*Exp[w - (x - y)*z] +
  a^2*x*z*Exp[w - (x - y)*z] -
  a*x*z*Exp[w + (x - y)*z] + a^2*x*z*
  Exp[w + (x - y)*z]))/
  (a*Exp[-w + (x - y)*z] + (1 - a)*
  Exp[-w - (x - y)*z])) -
  (a*Exp[-w + (x - y)*z]*
  ((1 - a)*z*Exp[-w - (x - y)*z] -
  a*z*Exp[-w + (x - y)*z])*(-((1 - a)*w) -
  2*w*a^2 + 2*w*a^3 + a^2*w*Exp[w - (x - y)*z] -
  a^3*w*Exp[w - (x - y)*z] +
  a^2*w*Exp[w + (x - y)*z] -
  a^3*w*Exp[w + (x - y)*z] + a*z - a^2*z +
  a*z*Exp[2*w] + a^2*z*Exp[2*(x - y)] -
  a*z*Exp[w - (x - y)*z] +
  a^2*z*Exp[w - (x - y)*z] -
  a*z*Exp[w + (x - y)*z] -
  a^2*z*Exp[w + (x - y)*z] + 2*a*x*z -
  2*a^2*x*z - a*x*z*Exp[w - (x - y)*z] +
  a^2*x*z*Exp[w - (x - y)*z] -
  a*x*z*Exp[w + (x - y)*z] +
  a^2*x*z*Exp[w + (x - y)*z]))/
  (a*Exp[-w + (x - y)*z] + (1 - a)*
  Exp[-w - (x - y)*z])^2 +
  (a*Exp[-w + (x - y)*z]*(-2*a^2*z*Exp[2*(x - y)] +
  a^2*w*z*Exp[w - (x - y)*z] -
  a^3*w*z*Exp[w - (x - y)*z] -
  a^2*w*z*Exp[w + (x - y)*z] +
  a^3*w*z*Exp[w + (x - y)*z] -
  a*z^2*Exp[w - (x - y)*z] +
  a^2*z^2*Exp[w - (x - y)*z] +
  a*z^2*Exp[w + (x - y)*z] +
  a^2*z^2*Exp[w + (x - y)*z] -
  a*x*z^2*Exp[w - (x - y)*z] + a^2*x*z^2*
  Exp[w - (x - y)*z] + a*x*z^2*
  Exp[w + (x - y)*z] - a^2*x*z^2*
  Exp[w + (x - y)*z]))/(a*Exp[-w + (x - y)*z] +
  (1 - a)*Exp[-w - (x - y)*z]) == 0;

Reduce[{eqn1, eqn2}, {x, y}]

Regards,
Jean-Marc


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