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Various New Expressions for Subresultants and Their Applications

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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.

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Authors and Affiliations

  1. Dpto. de Matematica Aplicada, Universidad de Murcia, 30071, Murcia, Spain

    Gema M. Diaz–Toca

  2. Dpto. de Matematicas, Estadistica y Comp., Universidad de Cantabria, Spain

    Laureano Gonzalez–Vega

Authors
  1. Gema M. Diaz–Toca
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  2. Laureano Gonzalez–Vega
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Correspondence to Gema M. Diaz–Toca.

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Partially supported by the European Union funded project RAAG (HPRN–CT–2001–00271) and by the spanish grant BFM2002-04402-C02-0

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Diaz–Toca, G., Gonzalez–Vega, L. Various New Expressions for Subresultants and Their Applications. AAECC 15, 233–266 (2004). https://doi.org/10.1007/s00200-004-0158-4

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  • DOI: https://doi.org/10.1007/s00200-004-0158-4

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