On the computation of minimal polynomials
type: Item
instance of: scholarly article
title: On the computation of minimal polynomials
zbMATH Open document ID: 0599.12026
DOI: 10.1016/0021-8693(86)90166-3
author: David R. Richman
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The author describes an algorithm for computing the polynomial p(X,Y) of minimal degree such that \(p(f,g)=0\), where f and g are non-constant polynomials in one indeterminate with the coefficients in a field K with the property that char(K) does not divide the greatest common divisor of deg(f) and deg(g). He also obtains a new and nice proof of the epimorphism theorem of \textit{S. S. Abhyankar} and \textit{T.-t. Moh} [J. Reine Angew. Math. 276, 148-166 (1975; Zbl 0332.14004)] which avoids the appeal to the Newton-Puiseux expansion theorem.
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 14A05
zbMATH DE Number: 3966241
zbMATH Keywords: minimal polynomials
zbMATH Keywords: epimorphism theorem
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90166-3
OpenAlex ID: W2083855831
cites work: Q3215049
cites work: Q4097032
cites work: On the concept of approximate roots for algebra
cites work: A Method to Compute Minimal Polynomials
cites work: Q3244502
description: scientific article; zbMATH DE number 3966241