  The Thom-Boardman symbol was first introduced by Thom in 1956 to classify
singularities of differentiable maps. It was later generalized by Boardman to a
more general setting. Although the Thom-Boardman symbol is realized by a
sequence of non-increasing, nonnegative integers, to compute those numbers is,
in general, extremely difficult. In the case of polynomial multiplication maps,
Robert Varley conjectured that computing the Thom-Boardman symbol for
polynomial multiplication reduces to computing the successive quotients and
remainders for the Euclidean algorithm applied to the degrees of the two
polynomials. In this paper, we confirm this conjecture.
