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MathGroup Archive 2007

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Re: Enquirey

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74830] Re: Enquirey
  • From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 7 Apr 2007 04:02:13 -0400 (EDT)
  • References: <ev2anc$k85$1@smc.vnet.net> <4614EDF3.90308@gmail.com>

On 4/6/07, Rita Ray <rayrita1 at gmail.com> wrote:
> Hi Jean,
>
> Thank you for your response. I've tried the way you wrote me to solve the
> equation but Mathematica is showing this "Reduce::naqs: eqn1 && eqn2 is not
> a quantified system of equations and inequalities." I really don't
> understand what does it mean. It would be great help if you could tell me is
> there any way I could proceed.
>
> Thank you.
>
> Rita

Have you tried (cut and paste) the code I attached to my previous
reply? It contains syntactically correct Mathematica expressions.

Anyway, as some others and I pointed out, neither Solve nor Reduce are
able to solve this kind of transcendental equation. You should try a
numerical approach, which implies to give some numeric values to some
or all of your parameters (a, w, z ?). Consult the documentation for
NSolve and the likes. See some examples below.

In[1] =
 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}]

  Reduce::"nsmet" : "This system cannot be solved with the methods
available to Reduce. (ButtonBox[\"More\[Ellipsis]\", Rule[ButtonStyle,
\"RefGuideLinkText\"], Rule[ButtonFrame, None],
RuleDelayed[ButtonData, \"Reduce::nsmet\"]])"

Out[3] =
Reduce[{a - a^2 - a*E^(2*w) + a^2*E^(2*(x - y)) - a*E^(w - (x - y)*z)
+ a^2*E^(w - (x - y)*z) - a*E^(w + (x - y)*z) - a^2*E^(w + (x - y)*z)
+ 2*a*x - 2*a^2*x - a*E^(w - (x - y)*z)*x + a^2*E^(w - (x - y)*z)*x -
a*E^(w + (x - y)*z)*x + a^2*E^(w + (x - y)*z)*x - (2*a^2*w)/z +
(2*a^3*w)/z + a^2*E^(w - (x - y)*z)*(w/z) - a^3*E^(w - (x -
y)*z)*(w/z) + a^2*E^(w + (x - y)*z)*(w/z) - a^3*E^(w + (x -
y)*z)*(w/z) == 0, -((a*E^(-w + (x - y)*z)*z*((-(1 - a))*w - 2*a^2*w +
2*a^3*w + a^2*E^(w - (x - y)*z)*w - a^3*E^(w - (x - y)*z)*w + a^2*E^(w
+ (x - y)*z)*w - a^3*E^(w + (x - y)*z)*w + a*z - a^2*z + a*E^(2*w)*z +
a^2*E^(2*(x - y))*z - a*E^(w - (x - y)*z)*z + a^2*E^(w - (x - y)*z)*z
- a*E^(w + (x - y)*z)*z - a^2*E^(w + (x - y)*z)*z + 2*a*x*z -
2*a^2*(x*z) - a*E^(w - (x - y)*z)*(x*z) + a^2*E^(w - (x - y)*z)*x*z -
a*E^(w + (x - y)*z)*(x*z) + a^2*E^(w + (x - y)*z)*x*z))/((1 - a)*E^(-w
- (x - y)*z) + a*E^(-w + (x - y)*z))) - (a*E^(-w + (x - y)*z)*((1 -
a)*E^(-w - (x - y)*z)*z - a*E^(-w + (x - y)*z)*z)*((-(1 - a))*w -
2*a^2*w + 2*a^3*w + a^2*E^(w - (x - y)*z)*w - a^3*E^(w - (x - y)*z)*w
+ a^2*E^(w + (x - y)*z)*w - a^3*E^(w + (x - y)*z)*w + a*z - a^2*z +
a*E^(2*w)*z + a^2*E^(2*(x - y))*z - a*E^(w - (x - y)*z)*z + a^2*E^(w -
(x - y)*z)*z - a*E^(w + (x - y)*z)*z - a^2*E^(w + (x - y)*z)*z +
2*a*x*z - 2*a^2*(x*z) - a*E^(w - (x - y)*z)*(x*z) + a^2*E^(w - (x -
y)*z)*x*z - a*E^(w + (x - y)*z)*(x*z) + a^2*E^(w + (x -
y)*z)*x*z))/((1 - a)*E^(-w - (x - y)*z) + a*E^(-w + (x - y)*z))^2 +
(a*E^(-w + (x - y)*z)*(-2*a^2*E^(2*(x - y))*z + a^2*E^(w - (x -
y)*z)*w*z - a^3*E^(w - (x - y)*z)*w*z - a^2*E^(w + (x - y)*z)*w*z +
a^3*E^(w + (x - y)*z)*w*z - a*E^(w - (x - y)*z)*z^2 + a^2*E^(w - (x -
y)*z)*z^2 + a*E^(w + (x - y)*z)*z^2 + a^2*E^(w + (x - y)*z)*z^2 -
a*E^(w - (x - y)*z)*x*z^2 + a^2*E^(w - (x - y)*z)*x*z^2 + a*E^(w + (x
- y)*z)*x*z^2 - a^2*E^(w + (x - y)*z)*x*z^2))/((1 - a)*E^(-w - (x -
y)*z) + a*E^(-w + (x - y)*z)) == 0}, {x, y}]

In[4] =
NSolve[{eqn1, eqn2} /. a -> 1, {x, y}]

  Solve::"ifun" : "Inverse functions are being used by (Solve), so
some solutions may not be found; use Reduce for complete solution
information. (ButtonBox[\"More\[Ellipsis]\", Rule[ButtonStyle,
\"RefGuideLinkText\"], Rule[ButtonFrame, None],
RuleDelayed[ButtonData, \"Solve::ifun\"]])"

  Solve::"svars" : "Equations may not give solutions for all \"solve\"
variables. (ButtonBox[\"More\[Ellipsis]\", Rule[ButtonStyle,
\"RefGuideLinkText\"], Rule[ButtonFrame, None],
RuleDelayed[ButtonData, \"Solve::svars\"]])"

Out[4] =
{{y -> Log[-((1.*E^(-1.*w + x)*Sqrt[-2. + z])/Sqrt[z])]}, {y ->
Log[E^(-1.*w + x)*(Sqrt[-2. + z]/Sqrt[z])]}}

In[5] =
NSolve[{eqn1, eqn2} /. a -> 1 /. z -> 1, {x, y}]

  Solve::"ifun" : "Inverse functions are being used by (Solve), so
some solutions may not be found; use Reduce for complete solution
information. (ButtonBox[\"More\[Ellipsis]\", Rule[ButtonStyle,
\"RefGuideLinkText\"], Rule[ButtonFrame, None],
RuleDelayed[ButtonData, \"Solve::ifun\"]])"

  Solve::"svars" : "Equations may not give solutions for all \"solve\"
variables. (ButtonBox[\"More\[Ellipsis]\", Rule[ButtonStyle,
\"RefGuideLinkText\"], Rule[ButtonFrame, None],
RuleDelayed[ButtonData, \"Solve::svars\"]])"

Out[5] =
{{y -> -1.*Log[E^w] + Log[E^x]}}

Regards,
Jean-Marc



> On 4/5/07, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> > 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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