Work

Differentiation of resultants and common multiple roots of polynomials

Year: 2024

Type: article

Abstract: In the article it is proven that once polynomials f and g possess a common root w of multiplicity s for f and multiplicity p for g, the Taylor series expansion for their resultant R = R (f , g)(g , b) in variables b (coefficients g) starts with the summand of order s, and the Taylor series expansion for R = R (f , g)(g , b) in variables a (coefficients f) starts with the summand of order p; and the explicit formulas for the corresponding summands of the Taylor series are obtained. Based on this, a number of results linking higher derivatives of resultants and multiple common roots of polynomials, which differ in ideas from the well-known ones, are obtained.

Source: Doklady of the National Academy of Sciences of Belarus

DOI: 10.29235/1561-8323-2024-68-4-282-287

Authors: A. V. Lebedev, Yu. V. Trubnikov, M. M. Chernyavsky

Institutions: Belarusian State University, Vitebsk State University named after P.M. Masherov

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Belarusian Republican Foundation for Fundamental Research

OpenAlex ID: W4402335038

FWCI: 0.201

Cites: 1

Cited by: 1

Related to: 10