Characterization of the symmetry class of an elasticity tensor using polynomial covariants

We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is cornerstone theory toy model for linear constitutive laws in physics. The novelty that these are written using polynomial covariants. As corollary, we deduce classes affine algebraic sets, result seems be new. Meanwhile, have been lead produce minimal set 70 generators covariant algebra harmonic introduce original generalized cross-product on totally symmetric tensors. Finally, tensorial covariants, new 294 invariant tensor.