The function Killing_eqns(T, coord, Cf2 ) computes the expressions for Killing's equations for each component of the totally symmetric covariant tensor T.  Specifically, the symmetric part of the covariant derivative of T is computed and returned as a tensor_type. The components of T satisfy Killing's equations if all of the components of the result are zero.  Note that the rank of the result is one more than that of T.

This routine is useful in two ways:  first, as a means of verifying that a tensor satisfies Killing's equations, and second, as a way of generating the differential equations for any unknown components of a symmetric tensor which is to satisfy Killing's equations.

T must be of rank 1 or greater.  If T is of second rank or more, the component array of T must use Maple's symmetric indexing function (since T must be symmetric).

Cf2 should be indexed using the cf2 indexing function provided by the tensor package.  It can be computed using the Christoffel2 routine.

Simplification:  This routine uses the `tensor/cov_diff/simp` and `tensor/lin_com/simp` routines for simplification purposes.  The simplification routines are used indirectly by the symmetrize and cov_diff procedures as they are called by Killing_eqns.  By default, `tensor/cov_diff/simp` and `tensor/lin_com/simp` are initialized to the `tensor/simp` routine.  It is recommended that these routines be customized to suit the needs of the particular problem.