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

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)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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