I am doing this work by hand, but it takes a lot of time and I make several calculation errors, so I was thinking to make Mathematica to calculate this for me, but I am stuck at the very beginning.
I am working with tensors like this:
$XXV_{ijk} = \dfrac{1}{6}(X_iX_jV_k+X_iX_kV_j+X_jX_iV_k+X_kX_jV_i+X_jX_kV_i+X_kX_iV_j)$ $-\dfrac{1}{5}(\delta_{ij}\, (X\cdot X) V_k+\delta_{ik} (X\cdot V) X_j+\delta_{jk} (X\cdot V) X_i)$
where $X_i$ and $V_i$ are the components of the 3-vectors $\vec{X}$ and $\vec{V}$. I have to multiply these tensors, for example
$XXV \times XXV = \dfrac{2}{25}V^2+\dfrac{8}{25} (X\cdot V)^2$
I think I can obtain the first part with Tuples
and Total
(?) but I don't know how to obtain the part with the Kroeneker deltas; if I can write these tensors correctly I think I can multiply these tensors with .
and Transpose
.
As @yarchik has pointd out, I have to add that my tensors have unit length