Diagonalizable higher degree forms and symmetric tensors

We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers independent linear forms, or equivalently, decomposing symmetric tensors into rank-1 linearly vectors. The rely on two facets higher degree namely Harrison's algebraic theory some algebro-geometric properties. proposed are based purely solving quadratic equations. Moreover, a byproduct our one can easily decide whether not polynomial tensor is orthogonally unitarily decomposable.