Symmetric trace-free tensors are used in many areas of physics, including
electromagnetism, relativistic celestial mechanics and geodesy, as well as in
the study of gravitational radiation and gravitational lensing. Their use
allows integration of the relevant wave propagation equations to arbitrary
order. We present an improved iterative method for the trace-free decomposition
of symmetric tensors of arbitrary rank. The method can be used both in
coordinate-free symbolic derivations using a computer algebra system and in
numerical modeling. We obtain a closed-form representation of the trace-free
decomposition in arbitrary dimensions. To demonstrate the results, we compute
the coordinate combinations representing the symmetric trace-free (STF) mass
multipole moments for rank 5 through 8, not readily available in the

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