## plotting – Determining intersection point in mathematica plot

I plotted the function given in the figure with respect to “z” .I obtained different plots for different distinct values of “t”.

Now please can you help how to obtain the intersection point of the straight line and the curves.I.e how to precisely obtain the value of ” z” at each intersection point.
Actually I am using mathematica online.So some sorts of code to obtain the intersection point will be helpfull.

Thank you

## plotting – How to plot several plots of numerical solutions on one graph

I have a coupled first order system of differential equations which I’m solving numerically (my actual system is more complicated so I use this simple example). I’m trying to plot the solutions for different values of $$n$$ on one graph:

``````sol = Table({n,
NDSolve({y'(x) + n z(x) == 0, z'(x) - n y(x) == 0, y(0) == 1,
z(0) == 1}, {y, z}, {x, 0, 1})}, {n, 1, 2})
Plot(Evaluate(y(x) /. sol((1))((2))), {x, 0, 1}, PlotRange -> All)
Plot(Evaluate(y(x) /. sol((2))((2))), {x, 0, 1}, PlotRange -> All)
Plot(Table(Evaluate(y(x) /. sol((n))((2))), {n, 1, 2}), {x, 0, 1},
PlotRange -> All)
``````

The last line doing this gives me an error “Part::pkspec1: The expression n cannot be used as a part specification.” However I can still plot solutions for different $$n$$s on different graphs, as illustrated by running the previous two lines. What is going wrong and how do I fix it?

Thanks in advance for any help.

## How to make a 4-dimensional plot?

`The following code represents the sets of inequalities that I want to show in a region plot. It has four parameters. The acceptable range for the 4 parameters is given by:{e, 0, 10}, {Subscript(c, I), 0, 10}, {Subscript(c, F), 0, 10}, {Subscript((Phi), F), 0, 10}. It would be very helpful if someone could help me in creating a region plot for these inequalities. Thank you so much. Please let me know if you want me to share any other information with you / edit something to match the formatting requirements. Thank you.’

``````    14.4321 && ((Subscript(c, I) < Subscript(c,
F) <= -2.32572*10^-44 (-6.42818*10^44 +
3.74953*10^43 Subscript(c, I)) +
2.77669*10^-92 Sqrt(
1.54894*10^186 - 1.26443*10^185 Subscript(c, I) +
2.23141*10^183
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) &&
0 <= e < Subscript(c, I) &&
Subscript((Phi), F) >=
9.09474*10^-140 (2.92819*10^141 - 2.49452*10^140 e +
3.48467*10^138 e^2 + 3.40329*10^139 Subscript(c, I) -
9.00261*10^136 e Subscript(c, I) - 4.98887*10^137
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
9.01935*10^139 Subscript(c, F) -
5.04169*10^138 e Subscript(c, F) -
2.19261*10^137 Subscript(c, I) Subscript(c, F) -
3.01648*10^138
!(*SubsuperscriptBox((c), (F), (2))))) || (-2.32572*10^-44
(-6.42818*10^44 + 3.74953*10^43 Subscript(c, I)) +
2.77669*10^-92 Sqrt(
1.54894*10^186 - 1.26443*10^185 Subscript(c, I) +
2.23141*10^183
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) <
Subscript(c,
F) < -8.89854*10^-31 (-1.68006*10^31 +
4.08425*10^28 Subscript(c, I)) +
3.52626*10^-59 Sqrt(
9.6042*10^119 + 8.19945*10^117 Subscript(c, I) -
1.31944*10^116
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) && ((0 <=
e < 1.35168*10^-42 (2.64803*10^43 +
9.55663*10^39 Subscript(c, I) +
5.35196*10^41 Subscript(c, F)) -
1.41645*10^-91 Sqrt(
2.19712*10^184 - 4.40692*10^182 Subscript(c, I) +
7.14401*10^180
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
1.29105*10^183 Subscript(c, F) +
4.06766*10^180 Subscript(c, I) Subscript(c, F) +
6.9229*10^181
!(*SubsuperscriptBox((c), (F), (2)))) &&
Subscript((Phi), F) >=
9.09474*10^-140 (2.92819*10^141 - 2.49452*10^140 e +
3.48467*10^138 e^2 + 3.40329*10^139 Subscript(c, I) -
9.00261*10^136 e Subscript(c, I) - 4.98887*10^137
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
9.01935*10^139 Subscript(c, F) -
5.04169*10^138 e Subscript(c, F) -
2.19261*10^137 Subscript(c, I) Subscript(c, F) -
3.01648*10^138
!(*SubsuperscriptBox((c), (F), (2))))) || (1.35168*10^-42
(2.64803*10^43 + 9.55663*10^39 Subscript(c, I) +
5.35196*10^41 Subscript(c, F)) -
1.41645*10^-91 Sqrt(
2.19712*10^184 - 4.40692*10^182 Subscript(c, I) +
7.14401*10^180
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
1.29105*10^183 Subscript(c, F) +
4.06766*10^180 Subscript(c, I) Subscript(c, F) +
6.9229*10^181
!(*SubsuperscriptBox((c), (F), (2)))) <= e < Subscript(c,
I) && Subscript((Phi), F) >= 0))) || (Subscript(c,
F) >= -8.89854*10^-31 (-1.68006*10^31 +
4.08425*10^28 Subscript(c, I)) +
3.52626*10^-59 Sqrt(
9.6042*10^119 + 8.19945*10^117 Subscript(c, I) -
1.31944*10^116
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) &&
0 <= e < Subscript(c, I) &&
Subscript((Phi), F) >= 0))) || (14.4321 <= Subscript(c, I) <
49.1997 && ((Subscript(c, I) < Subscript(c,
F) < -8.89854*10^-31 (-1.68006*10^31 +
4.08425*10^28 Subscript(c, I)) +
3.52626*10^-59 Sqrt(
9.6042*10^119 + 8.19945*10^117 Subscript(c, I) -
1.31944*10^116
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) && ((0 <=
e < 1.35168*10^-42 (2.64803*10^43 +
9.55663*10^39 Subscript(c, I) +
5.35196*10^41 Subscript(c, F)) -
1.41645*10^-91 Sqrt(
2.19712*10^184 - 4.40692*10^182 Subscript(c, I) +
7.14401*10^180
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
1.29105*10^183 Subscript(c, F) +
4.06766*10^180 Subscript(c, I) Subscript(c, F) +
6.9229*10^181
!(*SubsuperscriptBox((c), (F), (2)))) &&
Subscript((Phi), F) >=
9.09474*10^-140 (2.92819*10^141 - 2.49452*10^140 e +
3.48467*10^138 e^2 + 3.40329*10^139 Subscript(c, I) -
9.00261*10^136 e Subscript(c, I) - 4.98887*10^137
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
9.01935*10^139 Subscript(c, F) -
5.04169*10^138 e Subscript(c, F) -
2.19261*10^137 Subscript(c, I) Subscript(c, F) -
3.01648*10^138
!(*SubsuperscriptBox((c), (F), (2))))) || (1.35168*10^-42
(2.64803*10^43 + 9.55663*10^39 Subscript(c, I) +
5.35196*10^41 Subscript(c, F)) -
1.41645*10^-91 Sqrt(
2.19712*10^184 - 4.40692*10^182 Subscript(c, I) +
7.14401*10^180
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2))) +
1.29105*10^183 Subscript(c, F) +
4.06766*10^180 Subscript(c, I) Subscript(c, F) +
6.9229*10^181
!(*SubsuperscriptBox((c), (F), (2)))) <= e < Subscript(c,
I) && Subscript((Phi), F) >= 0))) || (Subscript(c,
F) >= -8.89854*10^-31 (-1.68006*10^31 +
4.08425*10^28 Subscript(c, I)) +
3.52626*10^-59 Sqrt(
9.6042*10^119 + 8.19945*10^117 Subscript(c, I) -
1.31944*10^116
!(*SubsuperscriptBox((c), ((ImaginaryI)), (2)))) &&
0 <= e < Subscript(c, I) &&
Subscript((Phi), F) >= 0))) || (Subscript(c, I) >= 49.1997 &&
Subscript(c, F) > Subscript(c, I) && 0 <= e < Subscript(c, I) &&
Subscript((Phi), F) >= 0)```

``````

## plotting – How do i use Streamplot to plot a non homogenous differential equation

I have the following equations:

x’ = x-y
y’ = x+y-2xy

I used the following code to do the streamplot: I apologize for only having an image, as I am using Mathematica through my school servers I cannot copy and paste the data.

But I do not get any results, so then I linearize the equations and plot them separately, but I cannot figure out how to combine the plots to show in one plot.:

Is there any way to use Streamplot with nonhomogenous DE’s or a better way to combine the equations?

## How to Plot two WordClouds next to each other?

I am confused on how to position two wordCloud graphs next to each other using Python and matplotlib library. What would be the step by step process on how to do this.

## plotting – Plot of a function defined on a differentiabl manifold

I’m following a course of Math and I would like to have a Plot of a 3D function defined over a CountorPlot. I used the command of ‘Plot3D’ to define the domain of a function but the region where the function f is defined is a differential manifold. There is an example:

f:3 x^2 – 2 y

manifold: x^3 – 3 x^2 y + y^2 – 1 == 0

I tried to visualize the intersection between the graphs using this code:

``````  aaa = ContourPlot3D[
x^3 - 3 x^2 y + y^2 - 1 == 0, {x, -10, 10}, {y, -10, 10}, {z, -10,
10}, PlotPoints -> 100]

bbb = Plot3D[ 3 x^2 - 2 y, {x, -10, 10}, {y, -10, 10},
PlotPoints -> 100]

Show[aaa, bbb]
``````

## plotting – Strange limitation of Z value of contour plot

I’m generating a figure using contourplot for my paper. The code is like this:

``````ContourPlot((x*y)/(240*10^-6+0.01x*((y-240*10^-6))), {x, 0, 50}, {y, 7/10^10, 4.5/
10^6}, ScalingFunctions -> {"Log", "Log", None}, Contours -> 100,
ContourStyle ->
Directive(GrayLevel(0), Opacity(0), AbsoluteThickness(0.005)),
ColorFunctionScaling -> True,
ColorFunction -> ColorData({"ThermometerColors", {0, 1}}),
PlotLegends -> Automatic)
``````

The contour it generated seems to have a strange upper limit due to the log scale of the figure. Because if I plot it with both X and Y axis being normal scale, it seems to be OK in terms of the upper limit.
Normal scale plot:

``````ContourPlot((x*y)/(
240*10^-6 + ((y - 240*10^-6)*0.01*x)), {x, 0, 50}, {y, 7/10^10, 4.5/
10^6}, ScalingFunctions -> {None, None}, Contours -> 100,
ContourStyle ->
Directive(GrayLevel(0), Opacity(0), AbsoluteThickness(0.005)),
ColorFunctionScaling -> True,
ColorFunction -> ColorData({"ThermometerColors", {0, 1}}),
PlotLegends -> Automatic)
``````

You can see if I use log scale the upper limit is about 0.018. But in the normal scale, the upper limit is 1.7.

What could be the problem? I’d like to use the Log scale for spreading up the values, can anyone help me to solve this issue to make the Z value for log scale figures also go to about 1.7?

Thank you so much!

## plotting – Equipotential surfaces using parametric plot

So I’m trying to plot lines on which the following function is a constant
$$frac{left(-Sigma (r,0.99,theta )+2 r^2-0.99^2 r sin ^2(theta )right)^2}{Delta (r,1,0.99) Sigma (r,0.99,theta )^3}+frac{0.99^4 sin ^2(theta ) cos ^2(theta ) Delta (r,1,0.99)}{Sigma (r,0.99,theta )^4}$$
where $$Delta (r,M,a):=a^2-2 M r+r^2quadtext{and}quadSigma (r,a,theta):=a^2 cos ^2(theta )+r^2.$$
I’m using the following code which was motivated from the second comment on this post

``````(CapitalSigma)(r_, a_, (Theta)_) := r^2 + a^2*Cos((Theta))^2;
(CapitalDelta)(r_, M_, a_) := r^2 - 2 M r + a^2;
cValues = {0.01, 0.1, 0.08, 0.06, 0.003, 0.005, 0.12, 0.14, 0.2, 0.15, 0.02, 0.04, 0.03, 0.18, 0.22, 1.5, 2.3, 0.002, 0.0025, 0.003, 0.0015, 0.0018, 0.0023, 0.0011, 0.0009, 0.0008, 0.0007, 0.0006, 0.0005};
trajectories = Function({x, y, r, (Theta)},  (CapitalSigma)(r, 0.99, (Theta))^(-3)*(CapitalDelta)(r, 1, 0.99)^(-1)*(2 r^2 - (CapitalSigma)(r, 0.99, (Theta)) - 0.99^2 r Sin((Theta))^2)^2 + (CapitalDelta)(r, 1, 0.99)*0.99^4*(CapitalSigma)(r, 0.99, (Theta))^(-4) Sin((Theta))^2 Cos((Theta))^2);
ParametricPlot({Sqrt(r^2 + 0.99^2)*Sin((Theta)), r Cos((Theta))}, {r, 0, 5}, {(Theta), 0, Pi/2}, PlotStyle -> {Green}, MeshFunctions -> {trajectories}, Mesh -> {cValues})
``````

and it gives the output as shown here (the second one is the zoomed out version of the first).

As you can see, the bottom left corner has strange behavior and I’m not sure why. I also do not understand what the `trajectories` part of this code is doing, more precisely why does the `Function` have 4 arguments in the beginning? Please help.

(context: I’m trying to plot the lines of constant acceleration in Kerr spacetime)

## plotting – Find points on a ellipse and plot the graph

For $$a=1.5$$, find the four points at which the ellipse

$$x^2/a^2+y^2/b^2=1$$

where $$a>0,, b>0$$ and intersects the curve $$a,b,pi=5$$.

Give your answers as exact values. Produce a plot showing the initial curve and the ellipse, with a large orange dot at each of the four intersection points.

I am very new to use the Mathematica and this website ;] I don’t know which command I should use. I will appreciate any help..

BTW, this is my classwork question and I just want to figure it out.

## plotting – Plot is cutting off axes labels

I am trying to create a plot with the axes labelled and for some reason the x axis label is getting cutoff. I’ve tried resizing the plot and it does not fix it. I am using the following code:

The data stored in allData is here, in case you want to recreate the problem.

`allData={{{1,0.00016`},{2,0.00006`},{4,8.`^-6},{8,7.`*^-6},{16,7.`^-6},{32,7.`*^-6},{64,6.`^-6},{128,7.`*^-6},{256,7.`^-6},{512,7.`*^-6},{1024,8.`^-6},{2048,0.00001`},{4096,0.000015`},{8192,0.000019`},{16384,0.00003`},{32768,0.000056`},{65536,0.000433`},{131072,0.00071`},{262144,0.001277`},{524288,0.002439`},{1048576,0.004779`},{2097152,0.009294`},{4194304,0.018461`},{8388608,0.036768`},{16777216,0.073468`}},{{1,0.000163`},{2,0.000094`},{4,6.`*^-6},{8,6.`^-6},{16,6.`*^-6},{32,6.`^-6},{64,6.`*^-6},{128,6.`^-6},{256,6.`*^-6},{512,6.`^-6},{1024,7.`*^-6},{2048,8.`^-6},{4096,0.000014`},{8192,0.000017`},{16384,0.00003`},{32768,0.000055`},{65536,0.000448`},{131072,0.000714`},{262144,0.001282`},{524288,0.002422`},{1048576,0.004701`},{2097152,0.009263`},{4194304,0.018312`},{8388608,0.036492`},{16777216,0.073259`}},{{1,0.000105`},{2,8.`*^-6},{4,2.`^-6},{8,2.`*^-6},{16,2.`^-6},{32,2.`*^-6},{64,2.`^-6},{128,2.`*^-6},{256,2.`^-6},{512,2.`*^-6},{1024,3.`^-6},{2048,5.`*^-6},{4096,9.`^-6},{8192,0.000014`},{16384,0.000025`},{32768,0.000048`},{65536,0.000393`},{131072,0.000731`},{262144,0.001266`},{524288,0.002407`},{1048576,0.004663`},{2097152,0.009127`},{4194304,0.018178`},{8388608,0.036096`},{16777216,0.071814`}},{{1,0.000105`},{2,0.000015`},{4,2.`*^-6},{8,2.`^-6},{16,2.`*^-6},{32,2.`^-6},{64,2.`*^-6},{128,2.`^-6},{256,2.`*^-6},{512,2.`^-6},{1024,2.`*^-6},{2048,5.`*^-6},{4096,0.000012`},{8192,0.000013`},{16384,0.000022`},{32768,0.00004`},{65536,0.00039`},{131072,0.000728`},{262144,0.001266`},{524288,0.002402`},{1048576,0.004629`},{2097152,0.009103`},{4194304,0.018147`},{8388608,0.036348`},{16777216,0.072373`}}}`