Invariant relations for the derivatives of two arbitrary polynomials. (English) Zbl 1260.13034

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 [I. M. Gel’fand, M. M. Kapranov and 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 \(b\in\mathbb{C}.\)


13P15 Solving polynomial systems; resultants


Zbl 0827.14036
Full Text: Euclid


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[2] V. V. Prasolov, Polynomials , Springer Verlag, New York, 2004.
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