Comment: It’s incomprehensible that a point of such importance (Symmetry, inflection, the solutions and critical points evaluation) isn’t mentioned within whole article. Moreover, the circle at Figure 4 is unnecessary dislocated above S(s,y_S) omitting even a vertical line up to the center of the circle as done at Figure 2 of “New approach …” by Nickalls R. W. D. (see note 29 again).  Tschirnhaus transformation isn’t only unneeded but also responsible for such a failure hence t_S = 0  doesn’t mean that an inflection point S(0,q) doesn’t exist. It seems to me reasonable the unknown t (along with the variables p and q) to be abandoned in favour of graphically grounded ones which are also easier for memorizing.