Double Sylvester sums for subresultants and multi-Schur functions

Authors:
Alain Lascoux;Piotr Pragacz
Affiliations:
C.N.R.S., Institut Gaspard Monge, Université de Marne-la-Vallée, 5 Bd Descartes, Champs sur Marne, F 77454 Marne La Vallée Cedex 2, France;Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, P.O. Box 21, PL 00-956 Warszawa 10, Poland
Venue:
Journal of Symbolic Computation
Year:
2003

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Abstract

Sylvester has announced formulas expressing the subresultants (or the successive polynomial remainders for the Euclidean division) of two polynomials, in terms of some double sums over the roots of the two polynomials. We prove Sylvester formulas using the techniques of multivariate polynomials involving multi-Schur functions and divided differences.