Title: Effective identifiability criteria for tensors and polynomials,
Abstract: 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
polynomial. Finally, we implement our identifiability algorithms in Macaulay2.