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MathGroup Archive 2012

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Re: Trying to close some loose plotting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124708] Re: Trying to close some loose plotting
  • From: Chris Young <cy56 at comcast.net>
  • Date: Wed, 1 Feb 2012 03:52:14 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jg5q7i$h4d$1@smc.vnet.net>

Here's a correction. My last posted version didn't plot on its own.

http://home.comcast.net/~cy56/Mma/RootsOfCubicPic3.png

http://home.comcast.net/~cy56/Mma/RootsOfCubic;6.nb


\[ScriptCapitalA][\[Mu]_, rc_] = Sqrt[
  4 (-3 + 2 \[Mu]^2)^3 + (27 rc - 18 \[Mu] + 20 \[Mu]^3)^2]^(1/3);

\[Lambda]1[\[Mu]_, rc_] =
  2 \[Mu] - (
   2*2^(1/3)*(-3 + 2 \[Mu]^2))/\[ScriptCapitalA][\[Mu], rc]^(1/3) +
   2^(2/3)*\[ScriptCapitalA][\[Mu], rc]/6;

\[Lambda]2[\[Mu]_, rc_] =
  1/12 (4*\[Mu] + (
     2*2^(1/3)*(1 + I Sqrt[3])*(-3 +
        2*\[Mu]^2))/\[ScriptCapitalA][\[Mu], rc]^(1/3) +
     2^(2/3)*(-1 + Sqrt[3] I)*\[ScriptCapitalA][\[Mu], rc]^(1/3));

\[Lambda]3[\[Mu]_, rc_] =
  1/12 (4*\[Mu] + (
     2*2^(1/3)*(1 - Sqrt[3] I)*(-3 +
        2*\[Mu]^2))/\[ScriptCapitalA][\[Mu], rc]^(1/3) -
     2^(2/3)*(1 + Sqrt[3] I)* \[ScriptCapitalA][\[Mu], rc]^(1/3));

thick = AbsoluteThickness[1.25];

rctab = {-2, -1, -0.5`, -0.3`, -0.15`, -0.08`, -0.04`, 0, 0.04`,
   0.08`, 0.15`, 0.3`, 0.5`, 1, 2};

Np = Length[rctab];

\[Lambda]1tab[\[Mu]_] =
  Table[\[Lambda]1[\[Mu], rc] /. rc -> rctab[[i]], {i, 1, Np}];
\[Lambda]2tab[\[Mu]_] =
  Table[\[Lambda]2[\[Mu], rc] /. rc -> rctab[[i]], {i, 1, Np}];
\[Lambda]3tab[\[Mu]_] =
  Table[\[Lambda]3[\[Mu], rc] /. rc -> rctab[[i]], {i, 1, Np}];

\[Lambda]123[\[Mu]_, rc_] =
  Flatten[{\[Lambda]1tab[\[Mu], rc], \[Lambda]2tab[\[Mu],
     rc], \[Lambda]3tab[\[Mu], rc]}];

Off[Plot::"plnr"];

Plot[
 Evaluate @ \[Lambda]1tab[\[Mu]],     {\[Mu], -1, 1},
 PlotStyle -> Table[Hue[0.8 (k - 1)/(Np - 1)], {k, 1, Np}],
 PlotRange -> {{-1.1, 1.1}, {-0.1, 12}},
 PlotPoints -> 300,
 MaxRecursion -> 6,
 AspectRatio -> 1/5 12.1/2.2,
 Frame -> True,
 FrameStyle -> LightGray,
 Axes -> False,
 ImageSize -> 300
 ]




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