A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics constructed from different sets of Jacobi vectors are derived and discussed. Moreover, an algorithm to directly determine the numbers of independent symmetric hyperspherical states (in case of bosonic systems) and antisymmetric hyperspherical-spinisospin states (in case of fermionic systems) entering the expansion of the A-body wave functions is presented. Numerical implementations for systems made with up to five bodies are reported.

中文翻译：

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计算对称或反对称超球面谐波的正交基

开发了一种建立适当对称超球面调和函数的正交基的数值方法。作为其中的一部分，推导出并讨论了用于计算由不同雅可比向量集构建的超球面谐波之间变换系数的改进算法。此外，还提出了一种直接确定进入 A 体波函数展开的独立对称超球面态（在玻色子系统的情况下）和反对称超球面-自旋自旋态（在费米子系统的情况下）数量的算法。报告了由多达五个实体组成的系统的数值实现。