Exercise 12, § 6

There exists a unique polynomial $P_{p,q}(T_0, \ldots, T_p, U_0, \ldots, U_q)$ with integer coefficients such that for every ring A and any polynomials $f = t_p X^p + \ldots + t_0, g = u_q X^q + \ldots + u_0$ of $\mathbf{A}[X]$ we have

If we assign the weight i to $T_i$ and $U_i$, then $P_{p,q}$ is isobaric of weight pq.