A converse rule of signs for polynomials
type: Item
instance of: scholarly article
title: A converse rule of signs for polynomials
zbMATH Open document ID: 0564.26004
DOI: 10.1007/BF02253324
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: Given a polynomial P(x), it is well-known that the Cardano-Descartes rule of signs gives only an upper bound on the number of its positive roots, except in the case in which there is one or no sign variation, where it indicates that P(x) has one or no positive root(s) respectively. In certain new root isolation methods, of great interest to symbolic mathematical computation, it is important to know under what conditions the existence of one positive root implies that P(x) presents only one sign variation. These conditions are discussed and presented in this paper.
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 68W99
zbMATH DE Number: 3899206
zbMATH Keywords: polynomial
zbMATH Keywords: Cardano-Descartes rule of signs
zbMATH Keywords: root isolation methods
zbMATH Keywords: symbolic mathematical computation
author: Alkiviadis G. Akritas
author: Stylianos D. Danielopoulos
MaRDI profile type: Publication
cites work: The fastest exact algorithms for the isolation of the real roots of a polynomial equation
cites work: On the forgotten theorem of Mr. Vincent
cites work: Q5536376
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description: scientific article; zbMATH DE number 3899206