Skew Symmetric Tensor Decomposition

We introduce the ``skew apolarity lemma" and we use it to give algorithms for the skew-symmetric rank and the decomposition 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 tri-tensor are also presented.