Mathematica, Plot Implicit function contain Sum (sigma)

[8s0nc1]

Dear friends,
Over the past week, I tried to plot implicit function by mathematica but failed. I am very disappointed. Hopefully someone help me at this time.
My equation is given by (see below figure):

Where
z0 := 6
d := 12
k := 11800
w0 := 0.025
w[z_] := sqrt[w0^2*(1 + (z/z0)^2)]
deltaphi0[z_] := 0.6/(1 + (z^2/z0^2))
R[z_] := z*(1 + (z0/z)^2)
wm0[z_] := sqrt[w^2/(2*m + 1)]
dm[z_] := (k/2)*((wm0)^2)
g[z_] := 1 + (d/R)
wm[z_] := wm0*sqrt[[g^2 + (d)^2/dm^2]]
Rm[z_] := d*(1 - g/(g^2 + (d/dm)^2))^(-1)
thetam[z_] := ArcTan[d/(dm*g)]
I want to plot a graph to represent the dependence of r (z). I have tried the following code-mathematica file

But mathamatica plot 2 coordinate axes without data (no points).

Please help me!
This is the mathematica file
https://docs.google.com/a/hcmus.edu.vn/file/d/0B6ue0CPI1AOFcWpjd19zMEU0a2s/edit
and my function
https://docs.google.com/a/hcmus.edu.vn/file/d/0B6ue0CPI1AOFTXMxRFZDaXd6NjQ/edit
Thanks very much.

 

[jackmell]

Quick look suggest you got that little s in there: First rule of Mathematica: all built-in functions names start with capital letters like Sqrt

 

[Bill Simpson]

I don't know how many more errors remain, but this fixes the first couple of waves and does plot something.

In[1]:= z0 = 6;
d = 12;
k = 11800;
w0 = 0.025;
w[z_] := Sqrt[w0^2*(1 + (z/z0)^2)];
deltaphi0[z_] := 0.6/(1 + (z/z0)^2);
R[z_] := z*(1 + (z0/z)^2);
wm0[z_] := Sqrt[w[z]^2/(2*m + 1)];
dm[z_] := k/2*wm0[z]^2;
g[z_] := 1 + d/R[z];
wm[z_] := wm0[z]*Sqrt[g[z]^2 + (d/dm[z])^2];
Rm[z_] := d/(1 - g[z]/(g[z]^2 + (d/dm[z])^2));
thetam[z_] := ArcTan[d/(dm[z]*g[z])];
ContourPlot[ Abs[ Sum[ (I*deltaphi0[z])^m/m!*wm0[z]/wm[z]* Exp[-r^2/wm[z]^2 - I*k*r^2/2*Rm[z] + I*thetam[z]], {m, 0, 1}]]^2 - 0.153*Abs[ Sum[ (I*deltaphi0[z])^m/m!*wm0[z]/wm[z]*Exp[I*thetam[z]], {m, 0, 1}]]^2 == 0, {r, -100, 100}, {z, -100, 100}]

Out[14]= ...PlotSnipped...

There are fairly clearly other things wrong. For example, when I change your plot range {r, -100, 100} to {r, -5, 5} to try to zoom in on the horizontal axis, instead of getting a substantially wider and more detailed version of your plot I get a narrower and narrower plot. So I think at least a couple of other things are seriously broken in the code.

 

[jackmell]

So I think at least a couple of other things are seriously broken in the code.

Great. That's a good start.

Now, to the poster:

How do we proceed from here? Well, I can tell you how to fix it without even looking at it: Start cutting things out, make it simpler while trying to keep the qualitative content of the code you're trying to run. Keep doing that even if you have to mercilessly hack it to death until it only vaguely resembles the original code. Get that simplified version running. Then piece by piece and not 2 or three at time, add one thing to the code, get it running, add another, get it running, then another until you build it back up to what you're trying to do.

 

[alphy]

Dear friend,

I understand your frustration with trying to plot the implicit function using Mathematica. It can be a complex process and requires a good understanding of the software and the mathematical equations involved. I would suggest reaching out to a colleague or a tutor who has experience with Mathematica to help you with your plot. You can also try looking for online tutorials or forums where others have successfully plotted implicit functions using Mathematica.

In terms of your specific equation, it is important to ensure that all the variables and functions are properly defined and inputted into the code. Double check the syntax and make sure there are no typos or errors. Also, consider breaking down the equation into smaller parts and plotting them individually to troubleshoot any issues that may arise.

Additionally, it may be helpful to provide more information on the specific error or issue you are encountering, as well as any error messages that Mathematica may be giving you. This will allow others to better understand the problem and provide more targeted solutions.

I hope you are able to successfully plot your implicit function and achieve your desired results. Don't give up and keep exploring different methods and resources to help you with your plot. Best of luck.