Reorganize Euclidean Tensors

[cortner]

This is to discuss whether we want to (1) entirely move away from putting Euclidean tensors into the coupling matrix and instead just apply a transform at the end; or (2) keep the euclidean tensors but replace the tables for the coco initial conditions with an implementation.

This is based on the following observation: there is a matrix A (easy to make explicit of course) such that x = r * A * Y1(x). This gives us in particular that a rotation matrix can be expanded as follows

Q_{ab} 
= (Q e^b)_a 
= sum_m A_am Y1m(Q e^b)
= sum_{m,j}  A_am D^1_mj(Q) Y1j(e^b)

I.e. we can explicitly express Q in terms of D^1 matrices and from here on the computation of the coupling coefficients could be automated. This can of course be extended to tensors of arbitrary order.

I think we should FOR SURE to (2), but even consider (1). What would the performance downside be? Is there a benefit to having less generality in the possible coupling coefficients?

CC @MatthiasSachs

[MatthiasSachs]

I see! Is that the approach Ralf Drautz describes in his paper?

[cortner]

(1) is Ralf's approach. (2) is to stick with our approach but just a neater way to compute the coupling coefficients

[cortner]

could actually be a nice BSc or MSc project if you know somebody?