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An elementary proof of Sylvester’s double sums for subresultants |
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| Authors: | Carlos D’Andrea Hoon Hong Teresa Krick Agnes Szanto |
| Affiliation: | 1. Department d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585; 08007, Spain;2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;3. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| 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. |
| Keywords: | Subresultants Double-sum formula Vandermonde determinant |
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