Invariant relations for the derivatives of two arbitrary polynomials (Q1925601)

The authors refresh the very well-known property of \(\mathrm{PGL}(2)\) invariance of the resultants of two polynomials in one variable (see for instance [\textit{I. M. Gel'fand, M. M. Kapranov} and \textit{A. V. Zelevinsky}, Discriminants, resultants, and multidimensional determinants. Mathematics: Theory \&{} Applications. Boston, MA: Birkhäuser. (1994; Zbl 0827.14036), (Chapter 12.1)]) to specify certain polynomial relations involving two univariate polynomials and their derivatives. The paper concludes with a research problem on how to decide with the right number of equations if two polynomials \(f(x)\) and \(q(x)\) satisfy \(f(x)=g(x+b)\) for some \(b\in\mathbb{C}.\)