  We introduce an algorithm to decide isomorphism between tensors. The
algorithm uses the Lie algebra of derivations of a tensor to compress the space
in which the search takes place to a so-called densor space. To make the method
practicable we give a polynomial-time algorithm to solve a generalization of
module isomorphism for a common class of Lie modules. As a consequence, we show
that isomorphism testing is in polynomial time for tensors whose derivation
algebras are classical Lie algebras and whose densor spaces are 1-dimensional.
The method has been implemented in the Magma computer algebra system.
