Re: Enquirey
- To: mathgroup at smc.vnet.net
- Subject: [mg74873] Re: Enquirey
- From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
- Date: Mon, 9 Apr 2007 06:15:23 -0400 (EDT)
- References: <ev2anc$k85$1@smc.vnet.net> <4614EDF3.90308@gmail.com>
On 4/7/07, Rita Ray <rayrita1 at gmail.com> wrote: > Hi Jean, > Thank you very much for your help. Yes, I've tried it once more and it is > working fine. But the problem is that the variable 'a' in my equation is > greater than 0.5 and less or equal to one. Therefore, I like to see how the > result changes if I change the value of 'a'. My 'z' is a postive no. I am > being trying to solve the equation with the changing value of 'a' but I > could not find it as Mathematica could not give me any answer. No error > message either. If you could give me some suggestions with that it would be > great help for me. > > Thank you for your time. > Rita [cross posted to MathGroup: comp.soft-sys.math.mathematica] Hi Rita, Without knowing what you did, it is going to be difficult to help in any meaningful way. You should post the code you tried alongside with any results and messages returned by Mathematica to MathGroup. You should use the *InputForm* when copying an expression from a Mathematica notebook to an email client. To do so, select the cell(s) you want to include in your email, then within the *Cell* menu select either *Convert To* or *Display As* and choose *InputForm*. Finally, copy and paste as usual. Also, you may be interesting in installing Ingolf Dahl's "SetFaceAndFont Palette," which, among many other useful things, provides a "CopyAsInputFormK button, for copying code with formatting removed." See http://library.wolfram.com/infocenter/MathSource/5752/ Regards, Jean-Marc > On 4/6/07, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote: > > 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 > > > > > > > > > > > > > >