Plotter for complex polynomials (complex coefficients)

• To: mathgroup at smc.vnet.net
• Subject: [mg124706] Plotter for complex polynomials (complex coefficients)
• From: Chris Young <cy56 at comcast.net>
• Date: Wed, 1 Feb 2012 03:51:32 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Not sure if this is done right. Could I speed it up by using Set
instead of SetDelayed in the converter to complex point? If so,
shouldn't I protect the "z" by wrapping the definition in a Module with
"z" as a local variable?

I have the coloring going from green for 0 to red for Ï? and then back
again, so colors are the same for plus and minus arguments (i.e.,
angles) for the complex polynomial. Probably should have some
indication which is which, or a way to toggle it.

http://home.comcast.net/~cy56/Mma/ComplexCoeffPlotter.nb
http://home.comcast.net/~cy56/Mma/ComplexCoeffPlotterPic2.png

Chris Young
cy56 at comcast.net

Manipulate[
Module[
{f, \[ScriptCapitalC]},

\[ScriptCapitalC][P_] := P[[1]] + P[[2]] I;   (*
Convert 2D point to complex point *)

f[z_] = \[ScriptCapitalC][a]  z^3 + \[ScriptCapitalC][
b] z^2 + \[ScriptCapitalC][c] z + \[ScriptCapitalC][ d];

Plot3D[
Abs[f[x + y I]],   {x, -6, 6},  {y, -6, 6},

PlotPoints -> 100,
MaxRecursion -> 2,

Mesh -> 11,
MeshStyle -> Directive[Gray, AbsoluteThickness[0.01]],
MeshFunctions -> ({x, y} \[Function] (\[Pi] -
Abs[Arg[f[x + I y]]])/\[Pi]),

ColorFunctionScaling -> False,
ColorFunction -> ({x, y} \[Function]
Hue[0.425 \[LeftFloor]12 (\[Pi] -
Abs[Arg[f[x + I y]]])/\[Pi]\[RightFloor]/12, sat, bri]),
PlotStyle -> Opacity[opac],
AxesLabel -> {"x", "i y", "|f(x + iy)|"}]
],
(*Item["The complex coefficients"],*)
{a, {-2, -2}, {2, 2}},
{b, {-2, -2}, {2, 2}},
{c, {-2, -2}, {2, 2}},
{d, {-2, -2}, {2, 2}},
{{opac, 0.75, "Opacity"}, 0, 1},
{{sat, 0.75, "Saturation"}, 0, 1},
{{bri, 1, "Brightness"}, 0, 1},

ControlPlacement -> {Left, Left, Left, Left, Bottom, Bottom, Bottom}
]

```

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