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MathGroup Archive 2004

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Re: Infrequent Mathematica User

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47055] Re: Infrequent Mathematica User
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Mon, 22 Mar 2004 22:39:10 -0500 (EST)
  • References: <c3mfek$r7l$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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

eqns = Thread[Simplify[
          D[f[x,y,z],#]& /@ {x,y,z}]==0];

FindRoot[eqns,{{x,1},{y,1},{z,1}}]

{x -> 0.6096239644159589, y -> 0.8626792159182006, 
  z -> 1.4545985039066525}

NSolve[eqns, {x,y,z}]

{{x -> -1.1504610099495616, y -> 2.389556579417945, 
   z -> -2.8343502221238883}, {x -> 1.1504610099495591, 
   y -> -2.3895565794179503, z -> 2.8343502221238954}, 
  {x -> -0.8844004241635046, y -> -2.0927346690454693, 
   z -> 2.4822776849670647}, {x -> 0.8844004241635126, 
   y -> 2.0927346690454627, z -> -2.482277684967057}, 
  {x -> 3.4547344369933075, y -> -2.649204308160977, 
   z -> -4.4669311049675535}, {x -> -3.454734436993219, 
   y -> 2.6492043081608667, z -> 4.466931104967412}, 
  {x -> -0.6096239644159579, y -> -0.8626792159182, 
   z -> -1.4545985039066518}, {x -> 0.6096239644159587, 
   y -> 0.8626792159181986, z -> 1.4545985039066525}}


Bob Hanlon

In article <c3mfek$r7l$1 at smc.vnet.net>, "Jim Dars" <jim-dars at comcast.net>
wrote:

<< f is a defined below as a function of x, y, and z.
I wish to take the partials set to zero and solve the 3 equations for x, y,
and z.
I've copied from Mathematica and had to clean up the paste, a bit.  I used
the partial symbol from the palette to define my partial derivatives.  The 3
lines on this page look nothing like what I feed Mathematica.
I've tried the "Solve equation" with just "a" and a[x_,y_,z_] etc.
Mathematica replies {{}}.
I sure would appreciate some advice.

Thanks, Best wishes, Jim
Jim-Dars at comcast.net

f[x_, y_, z_] =
      x/(1 + x^2) + y/(1 + x^2 + y^2) +
        z/(1 + x^2 + y^2 + z^2);
  a[x_, y_, z_] = \[PartialD]\_x f;\)\[IndentingNewLine]
  b[x_, y_, z_] = \[PartialD]\_y f;\)\[IndentingNewLine]
  c[x_, y_, z_] = \[PartialD]\_z\ f;\)\[IndentingNewLine]
  Solve[{a[x_, y_, z_] == 0, b[x_, y_, z_] == 0, c[x_, y_, z_] == 0}, {x, y,
      z}]
 >><BR><BR>


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