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Re: vertical lines in plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94236] Re: vertical lines in plot
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Mon, 8 Dec 2008 06:27:21 -0500 (EST)
  • Organization: University of Bergen
  • References: <ghavog$o8c$1@smc.vnet.net>

Cristina Ballantine wrote:
> In plotting the inverse image of the unit circle under the function B 
> below, I get all kinds of vertical lines. They are obviously jump 
> discontinuities, very likely caused by choices of branch cuts. I there any 
> way of getting rid of the vertical lines without redefining the brunch 
> cuts? I looked at the value of different solutions in sol4 close to a 
> point of discontinuity and it looks like the order of the solutions is 
> switched when t gets to that point. I am not sure if this is just a 
> coincidence. I also tried ExclusionsStyle->Red but there don't seem to be 
> any exclusions. 
> 
> 
> alpha := Pi/3
> r := 2/3
> a := r*Exp[I*alpha]
> n := 3
> 
> B[z] := 1/(z^n)*((Conjugate[a]/a)*(a^2 - z^2)/(1 - (Conjugate[a])^2*z^2))^n
> 
> sol4 := Solve[B[z] == Exp[I*t], z]
> 
> ParametricPlot[Evaluate[{Re[z], Im[z]} /. sol4], {t, 0, 2 Pi}, PlotRange -> All]
> 

Hello Cristina,

How about this alternative approach?

ContourPlot[Abs[B[x + I y]] == 1, {x, -3, 3}, {y, -3, 3},
  MaxRecursion -> 3]

Note that there is a little mistake in your code above---it is necessary 
to correct B[z] := ... to B[z_] := ... for this to work correctly.

Szabolcs


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