We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic of higher-order tensors subject to and genericity constraint. Reformulating this computational problem as system polynomial equations allows us leverage recent linear algebra tools from algebraic geometry. characterize complexity our in terms an property system—the multigraded regularity. prov...

We say that a first order formula Φ distinguishes a structure M over vocabulary L from another structure M ′ over the same vocabulary if Φ is true on M but false on M ′. A formula Φ defines an L-structure M if Φ distinguishes M from any other non-isomorphic L-structure M ′. A formula Φ identifies an n-element L-structure M if Φ distinguishes M from any other non-isomorphic n-element L-structure...