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Re: What do I do to get better curves?

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  • Subject: [mg120946] Re: What do I do to get better curves?
  • From: Bob Hanlon <hanlonr at>
  • Date: Thu, 18 Aug 2011 03:23:14 -0400 (EDT)
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  • Reply-to: hanlonr at

The function definitions should explicitly include all parameters.

p[k_, w_, r_] := Sqrt[w^2/r^2 - k^2];
q[k_, w_, r_] := Sqrt[w^2 - k^2];
a[k_, w_, p_, q_, r_] := (k^2 - w^2)^2 Sin[p] Cos[q] + 4 k^2 p q Cos[p] Sin[q];
a[k_, w_, r_] := a[k, w, p[k, w, r], q[k, w, r], r];

For the function to be real valued the arguments of the square roots must be nonnegative.

   Cases[a[k, w, r], Sqrt[z_] -> z, Infinity] > 0],
  k], {w >= 0, k >= 0, r > 1}]

k r < w

Checking the function value on the boundary

a[k, k*r, r]


Or equivalently,

a[w/r, w, r]


So the line k = w/r is part of the contour.

  Plot[w/r, {w, 0, 6}, PlotStyle -> Blue],
  ContourPlot[a[k, w, r] == 0, {w, 0, 6}, {k, 0, w/r},
   ContourStyle -> Directive[Red, AbsoluteThickness[2]]],
  AspectRatio -> 1,
  Frame -> True,
  Axes -> False,
  PlotRange -> {0, 6}],
 {{r, 6197/3122}, 1, 5, Appearance -> "Labeled"}]

Bob Hanlon

---- becko <becko565 at> wrote: 

Run the following code in mathematica:

a[k_,w_,p_,q_]:=(k^2-w^2)^2 Sin[p]Cos[q]+4k^2 p q Cos[p]Sin[q]

The curves thus obtained are very inaccurate. I tried raising the 
PlotPoints and WorkingPrecision opions of ContourPlot, but it doesn't 
work. Morevoer, you see that the only parameter that shows up, 'r', is 
an exact rational number. I don't know what else to try. Thanks.

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