The above properties of \( 6j \) symbols can again be tested using the symbolic python package wigner. Let us test the invariance $$ \begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6 \end{Bmatrix} = \begin{Bmatrix} j_2 & j_1 & j_3\\ j_5 & j_4 & j_6 \end{Bmatrix}. $$

The following program tests this relation for the case of \( j_1=3/2 \), \( j_2=3/2 \), \( j_3=3 \), \( j_4=1/2 \), \( j_5=1/2 \), \( j_6=1 \)