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
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
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v42_n3_p290_DAndrea_oai
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spelling I28-R145-paper_07477171_v42_n3_p290_DAndrea_oai2024-08-16 D'Andrea, C. Hong, H. Krick, T. Szanto, A. 2007 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. application/pdf http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Symb. Comput. 2007;42(3):290-297 Double-sum formula Subresultants Vandermonde determinant An elementary proof of Sylvester's double sums for subresultants info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v42_n3_p290_DAndrea_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
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
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v42_n3_p290_DAndrea_oai
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