An elementary proof of Sylvester's double sums for subresultants

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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 a...

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Autores principales: D'Andrea, C., Hong, H., Krick, T., Szanto, A.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2007
Materias:
Double-sum formula
Subresultants
Vandermonde determinant
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_07477171_v42_n3_p290_DAndrea2023-06-12T16:48:12Z An elementary proof of Sylvester's double sums for subresultants J. Symb. Comput. 2007;42(3):290-297 D'Andrea, C. Hong, H. Krick, T. Szanto, A. Double-sum formula Subresultants Vandermonde determinant 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. © 2006 Elsevier Ltd. All rights reserved. Fil:D'Andrea, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Double-sum formula
Subresultants
Vandermonde determinant
spellingShingle Double-sum formula
Subresultants
Vandermonde determinant
D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
An elementary proof of Sylvester's double sums for subresultants
topic_facet Double-sum formula
Subresultants
Vandermonde determinant
description 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. © 2006 Elsevier Ltd. All rights reserved.
format Artículo
Artículo
publishedVersion
author D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author_facet D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author_sort D'Andrea, C.
title An elementary proof of Sylvester's double sums for subresultants
title_short An elementary proof of Sylvester's double sums for subresultants
title_full An elementary proof of Sylvester's double sums for subresultants
title_fullStr An elementary proof of Sylvester's double sums for subresultants
title_full_unstemmed An elementary proof of Sylvester's double sums for subresultants
title_sort elementary proof of sylvester's double sums for subresultants
publishDate 2007
url http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
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AT szantoa anelementaryproofofsylvestersdoublesumsforsubresultants
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