Invariant relations for the derivatives of two arbitrary polynomials
type: Item
instance of: scholarly article
title: Invariant relations for the derivatives of two arbitrary polynomials
zbMATH Open document ID: 1260.13034
author: Arthur Holshouser
author: Harold Reiter
published in: Missouri Journal of Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mjms/1352138565
review text: 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 \(b\in\mathbb{C}.\)
reviewed by: Carlos D'Andrea
Mathematics Subject Classification ID: 13P15
zbMATH DE Number: 6116578
zbMATH Keywords: resultants
zbMATH Keywords: Sylvester matrix
zbMATH Keywords: invariants
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6116578