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 literature.

对称无迹张量用于物理学的许多领域，包括电磁学、相对论天体力学和大地测量学，以及引力辐射和引力透镜的研究。它们的使用允许将相关的波传播方程整合到任意阶。我们提出了一种改进的迭代方法，用于任意秩对称张量的无痕分解。该方法既可用于使用计算机代数系统的无坐标符号推导，也可用于数值建模。我们获得了任意维度的无痕分解的封闭形式表示。为了证明结果，我们计算了表示等级 5 到 8 的对称无痕 (STF) 质量多极矩的坐标组合，这在文献中不容易获得。