Assume you have a point cloud (stored in R
, 3xN dimensional matrix) in a 3D orthogonal coordinate system,
and you would like to derive analytical expressions for complicated functions of R (including differentiation, summations, etc.
As a simple example:
A_il(R)=\sum_jk df(R)/dR_ij df(R)/dR_kl
Is there any way to do this in sympy (or anything else...) with eg generalizing x,y,z
to X={x_i}, Y={y_i}, Z={z_i}
?
I would like to obtain general expression with Dirac deltas so that I do not need to handle all options separately. If it is an option I would prefer Einstein notation.
Thanks in anticipation
Responding to your comment here. Maybe this does what you want:
In [12]: X = IndexedBase('X')
In [13]: i, j = symbols('i, j')
In [14]: X[i].diff(X[j])
Out[14]:
δ
i,j