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I need to plot a complex implicit function, ContourPlot in this case is not very convenient for me. Therefore, I want to plot my function using discrete points. I think this simple approach is convenient, both for me to understand and for those who I want to help. So let's plot the unit circle using ListPlot. I can do it in this way (I'm sure there is much simpler way):

y[x_] := y /. FindRoot[x^2 + y^2 == 1, {y, 0.01}]
data = Table[{x, y[x]}, {x, -1, 1, 0.1}]
y2[x_] := y2 /. FindRoot[x^2 + y2^2 == 1, {y2, -0.01}]
data2 = Table[{x, y2[x]}, {x, -1, 1, 0.1}]
ListPlot[{data, data2}, PlotStyle -> {Black, Black}, AspectRatio -> 1]

Now I want to set constraint on the solution of y, say y < 0.5. How could I do this by using Select?

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Like Select[data, #[[2]] < .5 &]? –  belisarius Oct 29 '13 at 6:52
Yes, that's what I need. Thanks a lot –  Knightq Oct 30 '13 at 1:55
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1 Answer

Why bother with Select? Why not just change your Plot options to show what you want?

ListPlot[{data, data2},
  PlotRange -> {Full, {-1., 0.5}},
  PlotRangePadding -> 0.05,
  PlotStyle -> {{Black}},
  AspectRatio -> Automatic]


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Because that's just toy model, for the complex implicit function, I need to select out the solution with every small imaginary part. Thanks all the same. –  Knightq Oct 30 '13 at 1:58
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