Three questions1) Let's say that N ##q_i## and ##p_i## are transformed into ##Q_k## and ##P_k##, so that:
##q_i = q_i(Q_1,Q_2,. ... , P_1,P_2, ... ) ## and ##p_i=p_i((Q_1,Q_2,. ... , P_1,P_2, ... )##
We have proved that these transformations are canonical only and only if ##\forall i##...