Effective identifiability criteria for tensors and polynomials

A tensor T, in a given tensor space, is said to be h-identifiable if it admits a unique decomposition as a sum of h rank one tensors. A criterion for h-identifiability is called effective if it is satisfied in a dense, open subset of the set of rank h tensors. In this paper we give effective h-identifiability criteria for a large class of tensors. We then improve these criteria for some symmetric tensors. For instance, this allows us to give a complete set of effective identifiability criteria for ternary quintic polynomials. Finally, we implement our identifiability algorithms in Macaulay2.