By exhausting the symmetry partition and taking full advantage of simultaneous diagonalization to several matrices, we got some systems of orthogonal idempotents.

• 借助计算机穷举出所有可能的对称剖分，并利用多个矩阵同时对角化的技术，得到了许多定义在有限群的对称剖分上的正交幂等系统。