def riemann_cyclic_replace(t_r):
    """
    replace Riemann tensor with an equivalent expression

    ``R(m,n,p,q) -> 2/3*R(m,n,p,q) - 1/3*R(m,q,n,p) + 1/3*R(m,p,n,q)``

    """
    free = sorted(t_r.free, key=lambda x: x[1])
    m, n, p, q = [x[0] for x in free]
    t0 = S(2)/3*t_r
    t1 = - S(1)/3*t_r.substitute_indices((m,m),(n,q),(p,n),(q,p))
    t2 = S(1)/3*t_r.substitute_indices((m,m),(n,p),(p,n),(q,q))
    t3 = t0 + t1 + t2
    return t3
dataset/ETHPy150Open sympy/sympy/sympy/tensor/tensor.py/riemann_cyclic_replace/original