Theorem: sum_{g in Z_3} 1 - 3 = 0 (trivial-character orthogonality on Z_3)

Theorem (Schur-Z3-trivial-character canonical): for Z_3 with trivial character chi_0(g) = 1 for all g, the sum sum_{j=0}^{2} chi_0(j) chi_0*(j) = 1 + 1 + 1 = 3 = |Z_3|, satisfying the Schur orthogonality relation. Canonical sympy pin:…