       ParametricPlot precision problem

• To: mathgroup at smc.vnet.net
• Subject: [mg90869] ParametricPlot precision problem
• From: "Cristina Ballantine" <cballant at holycross.edu>
• Date: Sun, 27 Jul 2008 02:31:07 -0400 (EDT)

```Hi,

With the code below, plot1 gives a line from -a to 0 (in the complex
plane). plot2 should give the the symmetric of plot1 with respect to the
unit circle, i.e., a line from -1/Conjugate[a] to infinity (same slope as
line from -a to 0). I cannot get plot2 to give the correct line. Any help
is very much appreciated.

Cristina

---------------------------------

r := 1/3
alpha := Pi/3
a := r*Exp[I*alpha]
n := 3

B[z_] := z^n*((Conjugate[a]/a)*(a^2 - z^2)/(1 - (Conjugate[a])^2*z^2))^n

b := 1/(r*Sqrt)*Sqrt[3 - r^4 - Sqrt[(3 - r^4)^2 - 4*r^4]]*
Exp[I*alpha]

s := -Abs[B[b]]

z1[t_] := -(t/27) - ((1 + I Sqrt) (27 - 27 (-1)^(1/3) - t^2))/(
27 2^(2/3) (19602 t - 19602 (-1)^(1/3) t + 2 t^3 + Sqrt[
4 (27 - 27 (-1)^(1/3) - t^2)^3 + (19602 t - 19602 (-1)^(1/3) t +
2 t^3)^2])^(
1/3)) + ((1 - I Sqrt) (19602 t - 19602 (-1)^(1/3) t + 2 t^3 +
Sqrt[4 (27 - 27 (-1)^(1/3) - t^2)^3 + (19602 t -
19602 (-1)^(1/3) t + 2 t^3)^2])^(1/3))/(54 2^(1/3))

plot1:=ParametricPlot[{Re[z1[t]], Im[z1[t]]}, {t, s, 0},
PlotStyle -> {Orange, Thick}, PlotPoints -> 100, MaxRecursion -> 5,
PlotRange -> 1, WorkingPrecision -> 100]

plot2 :=
ParametricPlot[{Re[1/Conjugate[z1[t]]], Im[1/Conjugate[z1[t]]]}, {t,
s, 0}, PlotStyle -> {Orange, Thick}, PlotPoints -> 2000,
MaxRecursion -> 15, PlotRange -> All, WorkingPrecision -> 100]

```

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