Numerically set a logical whether a copula is symmetric (Nelsen, 2006, p. 38), or has exchangable variables, or is permutation symmetric (Joe, 2014, p. 66). A copula \(\mathbf{C}(u,v)\) is permutation symmetric if and only if for any \(\{u,v\} \in [0,1]\) the following holds
$$\mathbf{C}(u,v) = \mathbf{C}(v, u)\mbox{.}$$
The computation is (can be) CPU intensive.