  Functional bases, synonymous with separating sets, are usually formulated for
an entire vector space, such as the space Ela of elasticity tensors. We propose
here to define functional bases limited to symmetry strata, i.e. sets of
tensors of the same symmetry class. We provide such lowcardinal minimal bases
for tetragonal, trigonal, cubic or transversely isotropic symmetry strata of
the elasticity tensor.
