deriving equations for point clouds in sympy or alternatives

Question

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

I think that you need to break this down and start with a simpler question. — Oscar Benjamin, Jan 17 '20 at 14:28
OK, let's start with this can we define a vector of variables X={x_i}, such that it provides the property: Deriv[X,x_k]={DiracDelta(i,k)} — user2393987, Jan 20 '20 at 16:12

score 0 · Accepted Answer · answered Jan 20 '20 at 22:32

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

deriving equations for point clouds in sympy or alternatives

1 Answers1