An elementary proof of Sylvester's double sums for subresultants

Authors:
Carlos DAndrea;Hoon Hong;Teresa Krick;Agnes Szanto
Affiliations:
Department dÀ/lgebra i Geometria, Facultat de Matemà/tiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585/ 08007, Spain;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;Departamento de Matemá/tica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
Venue:
Journal of Symbolic Computation
Year:
2007

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Abstract

In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester's formula was also recently proved by Lascoux and Pragacz using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants.