×

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 \(b\in\mathbb{C}.\)

MSC:

13P15 Solving polynomial systems; resultants

Citations:

Zbl 0827.14036
PDFBibTeX XMLCite
Full Text: Euclid

References:

[1] E. J. Barbeau, Polynomials , (Problem Books in Mathematics) (Paperback), Springer Verlag, New York, 1989.
[2] V. V. Prasolov, Polynomials , Springer Verlag, New York, 2004.
[3] L. Weisner, Introduction to the Theory of Equations , Macmillan, New York, 1949.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.