Multiplicity of the solutions of a differential polynomial
type: Item
instance of: scholarly article
title: Multiplicity of the solutions of a differential polynomial
zbMATH Open document ID: 0860.12005
DOI: 10.1016/0022-4049(95)00045-3
published in: Journal of Pure and Applied Algebra
publication date: 1997-04-24T00:00:00Z
review text: Two notions of multiplicity for the solutions (Puiseux series) of differential polynomials are proposed. The first one is based on the Newton-Puiseux-Fine polygon, and it is of a combinatorial nature. The second one is of a differential nature and extends the standard notion of algebraic multiplicity. It is shown that both concepts, defined independently, are equivalent. The limit of the multiplicity for a given differential polynomial is also established, and a precise procedure to reduce the multiplicity is given. Finally, the problem of computability of these entries, which still remains open, is presented.
Mathematics Subject Classification ID: 12H20
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 13N10
zbMATH DE Number: 897487
zbMATH Keywords: multiplicity for solutions of differential polynomials
zbMATH Keywords: Puiseux series
zbMATH Keywords: reduction of multiplicity
zbMATH Keywords: Newton-Puiseux-Fine polygon
author: J. M. Farto
reviewed by: E. V. Pankrat'ev
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00045-3
OpenAlex ID: W1973526104
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description: scientific article; zbMATH DE number 897487