Resolvent representation for regular differential ideals
type: Item
instance of: scholarly article
title: Resolvent representation for regular differential ideals
zbMATH Open document ID: 1048.12005
author: Thomas Cluzeau
author: Evelyne Hubert
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2003-06-02T00:00:00Z
full work available at URL: RR-4200.pdf
review text: The authors provide a proof that the generic zeros of a differential ideal defined by a differential chain are birationally equivalent to the general zeros of a single regular differential polynomial, improving \textit{J. F. Ritt}'s resolvent theorem [cf. Differential algebra, Am. Math. Soc. (1950; Zbl 0037.18402)]. The result also generalizes the cyclic vector construction for a system of linear differential equations and also the rational univariate representation of algebraic zero dimensional radical ideals. Their methods of proof extend some results on differential dimension and relative order.
reviewed by: Vilmar Trevisan
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1922445
zbMATH Keywords: differential algebra
zbMATH Keywords: differential primitive element
zbMATH Keywords: cyclic vector
zbMATH Keywords: resolvent
describes a project that uses: ISOLATE
describes a project that uses: Kronecker
describes a project that uses: DIFFALG
MaRDI profile type: Publication
OpenAlex ID: W2016511760
DOI: 10.1007/S00200-002-0110-4
description: scientific article; zbMATH DE number 1922445