As I said in my other post, I have an implementation that will address this issue. However, I recommend against making the multiplication of a partial differential operator non-commutative, as this thinking comes from a fundamental misunderstanding (due to not knowing the difference between a differential operator and a differential form). The solution I will be implementing in Grassmann.jl is to use a basis for differential forms. Basically, you want to treat operator symbolic expressions separately from the dependent variables of a multivariable tensor field… the way to deal with this is to have a basis for differential operators and a basis for differential forms separately, which is exactly what my package is going to provide. Thus, multiplying differential operators with each other is different from multiplying differential operators and differential forms and commutativity doesn’t matter. As I mentioned before, this is not fully implemented yet. The solution you propose involves making the differential operator non-commutative, which is unnecessary once you understand the difference between differential operators and differential forms.
Anyway, you could easily define non-commutative operations in Julia without using any package, just use the Julia language it is already possible with the built-in language. My point is that this is the wrong idea for getting the behavior you want… what you want is differential operators and differential forms…
Not sure when I will implement this feature, but I’d like to be able to demonstrate it soon.