I have used MATLAB throughout my engineering. I had vector algebra course where we studied multiple vector algebra operations like gradient, curl and divergence in not just cartesian, but also cylindrical and spherical coordinates.
One of my friends needed an implementation of vector algebra in curvilinear coordinates for MATLAB. But the same was not available for MATLAB. So, I wrote a small toolbox for MATLAB to implement vector algebraic operations in other coordinate systems.
The method is simple. It uses symbolic computation where a vector system is first converted into cartesian. The vector operation is then performed in cartesian, followed by converting it back to the original coordinate system.
You can find my code on GitHub here.