Mathematica: Div in Cylindrical and Shadowing

[Saladsamurai]

Mathematica: Div in Cylindrical and "Shadowing"

I have a vector given in cylindrical coordinates. I know that the divergence of the vector should be zero. However, I am not sure why Mathematica is not returning zero. Also, the Div operator is showing up red (Div) and it is saying something about Shadowing. I have no idea what this means and the help is a little cryptic about it. I tried using Remove[Div] but it is protected. I am not sure what to do about that. This is the code i am using:

Clear["Global`*"]
Needs["VectorAnalysis`"]
Vr = (A/r^2 - B) Cos[theta];
Vtheta = (A/r^2 + B) Sin[theta];
Div[{Vr, Vtheta, 0}, Cylindrical[r, theta, z]]

which should give zero, but instead it gives me an algebraic expression.

 

[Bill Simpson]

For your red Div and warning search in this

http://reference.wolfram.com/mathematica/tutorial/Contexts.html

for red and read the explanation. Somehow you or perhaps VectorAnalysis has introduced a definition of Div that is going to be used before the built-in definition of Div and Mathematica is warning you about that.

Why your divergence isn't zero I haven't pursued.

 

[Bill Simpson]

For your red Div and warning search in this

http://reference.wolfram.com/mathematica/tutorial/Contexts.html

for red and read the explanation. Somehow you or perhaps VectorAnalysis has introduced a definition of Div that is going to be used before the built-in definition of Div and Mathematica is warning you about that.

Why your divergence isn't zero I haven't pursued.

Sorry, must have clicked twice, so edit this to add some additional information.

It isn't necessarily a bad thing that Div was redefined. VectorAnalysis may have broadened the definition or added new abilities. The reason for the warning when you tried to Remove[Div] is that for your safety most internal features have write/delete protection. If you really want to Remove[Div] you would have to Unprotect it first, but I would make certain that you know you need to do that and you understand the consequences. If VectorAnalysis did redefine Div then what it did was Unprotect, change the definition and then Protect it again.

 

[Oudeis Eimi]

I have a vector given in cylindrical coordinates. I know that the divergence of the vector should be zero. However, I am not sure why Mathematica is not returning zero. Also, the Div operator is showing up red (Div) and it is saying something about Shadowing. I have no idea what this means and the help is a little cryptic about it. I tried using Remove[Div] but it is protected. I am not sure what to do about that. This is the code i am using:

Clear["Global`*"]
Needs["VectorAnalysis`"]
Vr = (A/r^2 - B) Cos[theta];
Vtheta = (A/r^2 + B) Sin[theta];
Div[{Vr, Vtheta, 0}, Cylindrical[r, theta, z]]

which should give zero, but instead it gives me an algebraic expression.

Have you tried to simplify the result? Here's what I obtain in Mathematica 6:

In[1]:= Vr = (A/r^2 - B) Cos[theta];
Vtheta = (A/r^2 + B) Sin[theta];
divV = 1/r D[r Vr, r] + 1/r D[Vtheta, theta] // Simplify

Out[3]= 0

In[4]:= Needs["VectorAnalysis`"]
Div[{Vr, Vtheta, 0}, Cylindrical[r, theta, z]]

Out[5]= ((-B + A/r^2) Cos[theta] + (B + A/r^2) Cos[theta] - (
 2 A Cos[theta])/r^2)/r

In[6]:= % // Simplify

Out[6]= 0

 

[alphy]

Can you provide any insights on why this may be happening and how to resolve it?

I am familiar with Mathematica and its use for mathematical and scientific computations. In this case, it seems that there may be some conflicting definitions or functions within the Mathematica package that is causing the issue with the Div operator. The "Shadowing" error could be indicating that there are multiple definitions or functions for the Div operator and Mathematica is unsure which one to use.

One potential solution could be to explicitly specify which Div operator you want to use, such as Div[Cylindrical[r, theta, z], {Vr, Vtheta, 0}]. This will ensure that Mathematica uses the correct definition for the Div operator.

Another solution could be to use the Inactivate function to temporarily deactivate the Div operator and then use Activate to reactivate it after your calculations are done.

It is also possible that there may be a bug or error in the VectorAnalysis package itself. In this case, you could try reaching out to the package developers for further assistance.

Overall, it is important to carefully check the definitions and functions being used in your code and to consult with the Mathematica community or package developers for any issues or errors that you may encounter.