Given two symplectomorphisms $T_1: (q_1, p_1):\longrightarrow (q_2, p_2)$ and $T_2: (q_2, p_2):\longrightarrow (q_3, p_3)$ and corresponding generating functions $F_1(q_1, q_2)$ and $F_2(q_2, q_3)$, what is the formula for the generating function $F(q_1, q_3)$ of the composed symplectomorphism $T=T_2T_1:(q_1, p_1):\longrightarrow (q_3, p_3)$?