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Manipulate not working

• To: mathgroup at smc.vnet.net
• Subject: [mg101458] Manipulate not working
• From: danny <epstiend at gmail.com>
• Date: Wed, 8 Jul 2009 07:07:59 -0400 (EDT)

Hi, I'd like to illustrate the placement of (complex) roots of f(z)=z^2-4z+k in the complex plane along with the real surface of the function, a contour of the parabola, level contours where the real and complex components are zero, and two red dots showing the zeros as k ranges from -5 to 5.  The code works ok separately, but Manipulate chokes.  Perhaps it's too CPU intensive to work with Manipulate.  Can someone suggest ways of speeding it up.  Here's the code:

Manipulate[f[z_] := z^2 - 4*z + k; 
   rpts = Graphics3D[{PointSize[0.02], Red, 
      Point @@ {({Re[#1], Im[#1], 0} & ) /@ 
         (z /. Solve[f[z] == 0, z])}}]; 
   p1 = ParametricPlot3D[{Re[z], Im[z], Re[f[z]]} /. z -> x, 
     {x, 0, 4}, PlotStyle -> {Thickness[0.008], Yellow}]; 
   p2 = Plot3D[Re[f[z]] /. z -> x + I*y, {x, 0, 4}, 
     {y, -4, 4}, PlotRange -> {{0, 4}, {-2, 2}, {-5, 5}}, 
     PlotStyle -> {LightPurple}]; 
   cp1 = ContourPlot[Re[f[x + I*y]] == 0, {x, 0, 4}, 
     {y, -2, 2}]; lns = Cases[Normal[First[cp1]], 
     Line[pts_] :> ({#1[[1]], #1[[2]], 0} & ) /@ pts, 
     {0, Infinity}]; realcontour = 
    Show[Graphics3D[{Thickness[0.008], Purple, 
       Line @@ {lns}}], PlotRange -> {{0, 4}, {-2, 2}, 
       {-5, 5}}]; cp2 = ContourPlot[Im[f[x + I*y]] == 0, 
     {x, 0, 4}, {y, -2, 2}]; lns = Cases[Normal[First[cp2]], 
     Line[pts_] :> ({#1[[1]], #1[[2]], 0} & ) /@ pts, 
     {0, Infinity}]; imagcontour = 
    Show[Graphics3D[{Thickness[0.008], Green, 
       Line @@ {lns}}], PlotRange -> {{0, 4}, {-2, 2}, 
       {-5, 5}}]; realdiagram = 
    Show[{p2, p1, realcontour, imagcontour, rpts}, 
     PlotRange -> {{0, 4}, {-2, 2}, {-5, 5}}, 
     Lighting -> "Neutral", BoxRatios -> {1, 1, 1}, 
     AxesLabel -> {Style["x", 20], Style["y", 20], 
       Style["Re", 20]}, AxesEdge -> {{-1, -1}, {1, -1}, 
       {1, 1}}, ImageSize -> {500, 500}], {k, -5, 5, 1}]

• Follow-Ups:
  • Re: Manipulate not working
    • From: Murray Eisenberg <murray@math.umass.edu>