Comment on ``Poisson schemes for Hamiltonian systems on Poisson manifolds'' (Q1346837)

In the paper by \textit{W. Zhu} and \textit{M. Qin} [ibid. 27, No. 12, 7-16 (1994; Zbl 0807.58018)] the authors concluded that among the symplectic Runge-Kutta methods, only the diagonally implicit ones are Poisson. In this short remark the author shows that all symplectic Runge-Kutta methods are Poisson because Runge-Kutta methods are equivariant under linear maps.