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MathGroup Archive 2004

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Re: AW: Infrequent Mathematica User

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47071] Re: AW: Infrequent Mathematica User
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Tue, 23 Mar 2004 01:58:18 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <c3oc0r$8fe$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <c3oc0r$8fe$1 at smc.vnet.net>, Matthias.Bode at oppenheim.de 
wrote:

> applying the KIS principle, try:
> 
> Clear[x, y, z]
> func = x/(1 + x^2) + 
>     y/(1 + x^2 + y^2) + 
>     z/(1 + x^2 + y^2 + z^2); 
> dfx = D[func, x]; 
> dfy = D[func, y]; 
> dfz = D[func, z]; 
> Reduce[dfx == 0 && 
>    dfy == 0 && dfz == 0, x]
> N[%] 

Alternatively, one can use the built-in Del operator (which formats 
nicely in StandardForm or TraditionalForm):

  f[x_, y_, z_] = x/(x^2 + 1) + y/(x^2 + y^2 + 1) + 
    z/(x^2 + y^2 + z^2 + 1); 

  Del[f_] := {D[f, x], D[f, y], D[f, z]}

Reduce solves the equations (in terms of Root objects):

  Reduce[Del[f[x, y, z]] == 0, x]

NSolve yields high-precision numerical solutions directly:

  NSolve[Del[f[x, y, z]] == 0, {x, y, z}, WorkingPrecision -> 20]

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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