  We introduce the ``skew apolarity lemma'' and we use it to give algorithms
for the skew-symmetric rank and the decompositions of tensors in
{$\bigwedge^dV_{\mathbb{C}}$ with $d\leq 3$ and $\dim V_{\mathbb{C}} \leq 8$}.
New algorithms to compute the rank and a minimal decomposition of a tritensor
are also presented.
