Identifiability via Bertini and Macaulay2 software

A tensor is called identifiable if it admits a unique presentation in terms of simple tensors. This concept has many important applications in several areas (engineering, statistics, chemistry,...). After recalling main properties about tensor decomposition, we focus on the Waring setting and we show how Numerical Algebraic Geometry can help to detect (generic) identifiable cases, over the complex and real field. Moreover, we show that it is possible to go beyond the celebrated Kruskal's criterion in the case of specific complex tensors of order 4.