Re: Manipulate not working

• To: mathgroup at smc.vnet.net
• Subject: [mg101570] Re: [mg101458] Manipulate not working
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 10 Jul 2009 06:46:23 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200907081107.HAA12055@smc.vnet.net>

```What do you mean when you say that Manipulate is "choking" on the
Manipulate? I tried this with Mathematica 7.0.1 on a PC with a 3 GHz
Core 2 Duo CPU, 3 GB RAM, and 32-bit Windows XP Professional. AS soon as
I evaluated the Input cell, I could open the output's play controls,
click the Play button, and have the graphics cycle through all the
values of k in approximately 5 seconds.

danny wrote:
> 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}]
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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