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Questions on creating visualizations from functions or data using high-level constructors such as Plot, ListPlot, Histogram, etc.

4 votes
Accepted

How to draw this implicit function?

The equation x^2 - y^2 == Tan[y^x] is equivalent to the series of the equations ArcTan[x^2 - y^2] == y^x + k*Pi, where k∈ Integers. Therefore, ContourPlot[Evaluate[Table[ArcTan[x^2 - y^2] == y^x + k* …
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1 vote
4 answers
484 views

How to make plot of implicit function?

I try to produce a plot of $$\frac{1}{2}-\left| y\right| =\sqrt{\left(\frac{1}{2}-\left| y\right| \right)^2+(y-\sin (x))^2} $$ through ContourPlot[1/2 - Abs[y] ==Sqrt[(1/2 - Abs[y])^2+(y-Sin[x])^2], …
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  • 30.4k
2 votes
2 answers
150 views

Problem with Plot

The command Plot[Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]], {x, -Pi, Pi}] performs However, this result contradicts both calculus over the reals, where $\log_3(-\cos x)$ is not define …
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  • 30.4k
2 votes
0 answers
303 views

Problem with ImplicitRegion

Mathematica draws the domain RegionPlot[3^Sqrt[x] - 3^(2 Sqrt[y]) >= -Sqrt[x] + 2 Sqrt[y] && x^2 + y^2 <= 9 + 2 x y, {x, -0.1, 5}, {y, -0.1, 2}, PlotPoints -> 30] which is the triangle with the …
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2 votes

how to plot data which contains imaginary number

How about the following? ListPointPlot3D[{#[[1]], Re[#[[2]]], Im[#[[2]]]} & /@ data]
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1 vote

How to plot this set $M\subset\mathbb{R}^3$?

This can be done as follows. Region[ImplicitRegion[y == RealAbs[x] && 0 <= y < z, {x, y, z}]]
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5 votes
Accepted

Plotting an integral

NIntegrate instead of Integrate does the job: LogLogPlot[1.1183*3.086*10^-12 (c^(1/2))*2.598*10^-3 NIntegrate[ x^(1/2) Exp[-10.7* c/x] Sqrt[(1 - (125/1000)^2)*(1 - (2*4.18/125)^2) - (1 - (2 x/ …
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1 vote

ContourPlot fails with composite condition?

How about ContourPlot[Boole[x^2 + y^2 == 1 || x^2 + y^2 == 2], {x, -2, 2}, {y, -2, 2}] ? Please, play with color on your own.
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3 votes
0 answers
152 views

Do StreamPlot and VectorPlot work with Piecewise?

Executing StreamPlot[{Piecewise[{{-1, z < -1}, {z, 1 >= z && z >= -1}, {1, z > 1}}] , -x}, {z, -5, 5}, {x, -5, 5}] , I see an error message "Part::partw: Part 1 of {} does not exist." which I don't …
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0 votes
1 answer
336 views

Mathematica calendar for 2023 [closed]

Here is a Maple calendar for 2022 as an example. I am pretty sure there is a lot of nice Mathematica visualizations of deep math results which may be used for such a calendar for 2023. I am not strong …
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  • 30.4k
1 vote

Plot and mention extremum with corresponding points of extrema

Here are plots: ComplexPlot[Log[Abs[h[v]]], {v, 0 + 0*I, 10 - 10*I}] ComplexPlot3D[Log[Abs[h[v]]], {v, 0 + 0*I, 10 - 10*I},PlotPoints -> 50] It is difficult with the extrema since ComplexExpand[h[ …
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  • 30.4k
2 votes

ContourPlot is not accurately capturing contour lines

There is a workaround, at least for the case under consideration. ListPlot[{x, y} /.FindInstance[(x^2/4 + y^2 - 1)^2 == 0 && RealAbs[x] <= 2 && RealAbs[y] <= 2, {x, y}, Reals, 25000]]
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  • 30.4k
1 vote

How to plot the image of the unit disc under the mapping $f(z)=z/(1-z)$

This can be done with ComplexRegionPlot as follows. f[z_] := z/(1 - z); disk[z_] := Abs[z] <= 1 {ComplexRegionPlot[disk[z], {z, -3 - 3 I, 3 + 3 I}, PlotLabel -> z], ComplexRegionPlot[disk[InverseFun …
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1 vote

How to plot a complex functions in complex plane?

There are ComplexPlot and ComplexPlot3D commands since version 12 of Mathematica. See http://reference.wolfram.com/language/ref/ComplexPlot.html and http://reference.wolfram.com/language/ref/ComplexPl …
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3 votes
1 answer
299 views

how To Improve that ComplexPlot3D

I have in mind the result of ComplexPlot3D[Log[MittagLefflerE[1/2, z]],{z, -50 - 50*I, 50 + 50*I}, PlotPoints -> 300,PlotRange -> All] In particular, the plot should be seen over the whole quadr …
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