Subresultants of Several Univariate Polynomials in Newton Basis

In this paper, we consider the problem of formulating the subresultant polynomials for several univariate polynomials in Newton basis. It is required that the resulting subresultant polynomials be expressed in the same Newton basis as that used in the input polynomials. To solve the problem, we devi...

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Veröffentlicht in:	arXiv.org
Hauptverfasser:	Wang, Weidong, Yang, Jing
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 10.09.2024
Schlagworte:	Polynomials
ISSN:	2331-8422
Online-Zugang:	Volltext
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Zusammenfassung:	In this paper, we consider the problem of formulating the subresultant polynomials for several univariate polynomials in Newton basis. It is required that the resulting subresultant polynomials be expressed in the same Newton basis as that used in the input polynomials. To solve the problem, we devise a particular matrix with the help of the companion matrix of a polynomial in Newton basis. Meanwhile, the concept of determinantal polynomial in power basis for formulating subresultant polynomials is extended to that in Newton basis. It is proved that the generalized determinantal polynomial of the specially designed matrix provides a new formula for the subresultant polynomial in Newton basis, which is equivalent to the subresultant polynomial in power basis. Furthermore, we show an application of the new formula in devising a basis-preserving method for computing the gcd of several Newton polynomials.
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2212.03422