What is the correct use of TransformedField when the coordinate transformation is
"Cylindrical" -> "Cartesian"
?
When I do
TransformedField[
"Cylindrical" -> "Cartesian", {1, 1, 1}, {r, \[Theta], z} -> {x, y, z}]
I get nothing in return.
As I understand it, the problem is with the two zs in the "From" and "To" lists. Changing one of the z to something else, like \[Zeta] makes the function work:
TransformedField["Cylindrical" -> "Cartesian", {1, 1, 1}, {r, \[Theta], \[Zeta]} -> {x, y, z}]
(*{x/Sqrt[x^2 + y^2] - y/Sqrt[x^2 + y^2], x/Sqrt[x^2 + y^2] + y/Sqrt[x^2 + y^2], 1}*)
What if I am working on a field in cylindrical coordinates with explicit dependence on z, which I later want to transform into a field in Cartesian coordinates? In this instance I need to change every z to \[Zeta] and then call for TransformedField[].
Looks to me like Mathematica is smarter then this.
Is there any shorter way to do that?
