Various New Expressions for Subresultants and Their Applications

Authors:
Gema M. Diaz–Toca;Laureano Gonzalez–Vega
Affiliations:
Universidad de Murcia, Dpto. de Matematica Aplicada, 30071, Murcia, Spain;Estadistica y Comp., Universidad de Cantabria, Dpto. de Matematicas, 30071, Murcia, Spain
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2004

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Abstract

This article is devoted to presenting new expressions for Subresultant Polynomials, written in terms of some minors of matrices different from the Sylvester matrix. Moreover, via these expressions, we provide new proofs for formulas which associate the Subresultant polynomials and the roots of the two polynomials. By one hand, we present a new proof for the formula introduced by J. J. Sylvester in 1839, formula written in terms of a single sum over the roots. By other hand, we introduce a new expression in terms of the roots by considering the Newton basis.