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Re: I have A Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg14656] Re: [mg14621] I have A Problem
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Sat, 7 Nov 1998 02:10:04 -0500
• Organization: Universidad del Valle
• References: <199811041846.NAA19298@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Kale,
I would say you use the wrong method. If you try solving it by hand (I
mean using Mathematica but solving say the first equation for x, plug
it into the three equations left and so on you will realize quite soon
what you are expecting.
If you are just interested in solutions try this one:

In[1]:= f[x_,y_,u_,z_]={u^2-.75*x*(1+y+2*y^2+(1/3)*u*z+2*z^2),
                 .775*x*z+u-.25*u*x*(1+y+2*y^2+2*z^2),
                 9*u^2*y+3*u*z-.25*x*(1+6*y+3*y^3+3*y*z^2)-
                         1.5*u*x*z*(1+.5*y^2+.5*z^2),                
    9*u^2*z-3*u*y-1.5*x*(1+.5*y^2+.5*z^2)+.25*u*x*(1+6*y+3*y^3+3*y*z^2)}

In[2]:= tt=Table[FindRoot[
     
f[x,y,u,z]==0,{x,Random[Real,{-100,100}]},{y,Random[Real,{-100,100}]},{
       
u,Random[Real,{-100,100}]},{z,Random[Real,{-100,100}]}],{10000}];

(* You might want to change the range to search in. *)

In[3]:= tt1=Select[tt,Chop[f[x,y,u,z]/.#]=={0,0,0,0}&]; (* To kick out
the intents where FindRoot did not converge. *)

In[4]:= Sort[tt1]

Besides solutions of the (now) obvious type {x->0,u->0} I found:

{x\[Rule]2.22976,y\[Rule]0.0316221,u\[Rule]-1.32952,z\[Rule]0.265574}

and

{x\[Rule]4.34226,y\[Rule]0.0675919,u\[Rule]1.9589,z\[Rule]0.11501}

Jurgen


'Kale Oyedeji wrote:
> 
> The problem below continues for ever. What am I doing wrong?
> 
> 'Kale Oyedeji
> 
> > NSolve[{u^2-.75*x*(1+y+2*y^2+(1/3)*u*z+2*z^2)==0,
> >                 .775*x*z+u-.25*u*x*(1+y+2*y^2+2*z^2)==0,
> >                 9*u^2*y+3*u*z-.25*x*(1+6*y+3*y^3+3*y*z^2)-
> >                         1.5*u*x*z*(1+.5*y^2+.5*z^2)==0,
> >                 9*u^2*z-3*u*y-1.5*x*(1+.5*y^2+.5*z^2)+.25*u*x*(1+6*y+3*y^3+3*y*z^2)==0},{u,
> >     x,y,z}]
> >

• References:
  • I have A Problem
    • From: "'Kale Oyedeji" <koyedeji@morehouse.edu>