An elementary proof of Sylvester's double sums for subresultants

Autores
D'Andrea, C.; Hong, H.; Krick, T.; Szanto, A.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fuente
J. Symb. Comput. 2007;42(3):290-297
Materia
Double-sum formula
Subresultants
Vandermonde determinant
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_07477171_v42_n3_p290_DAndrea
Acceder
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oai_identifier_str paperaa:paper_07477171_v42_n3_p290_DAndrea
network_acronym_str BDUBAFCEN
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network_name_str Biblioteca Digital (UBA-FCEN)
spelling An elementary proof of Sylvester's double sums for subresultantsD'Andrea, C.Hong, H.Krick, T.Szanto, A.Double-sum formulaSubresultantsVandermonde determinantIn 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.2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndreaJ. Symb. Comput. 2007;42(3):290-297reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-04T09:48:28Zpaperaa:paper_07477171_v42_n3_p290_DAndreaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-04 09:48:32.956Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv An elementary proof of Sylvester's double sums for subresultants
title An elementary proof of Sylvester's double sums for subresultants
spellingShingle An elementary proof of Sylvester's double sums for subresultants
D'Andrea, C.
Double-sum formula
Subresultants
Vandermonde determinant
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 An elementary proof of Sylvester's double sums for subresultants
dc.creator.none.fl_str_mv D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author D'Andrea, C.
author_facet D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author_role author
author2 Hong, H.
Krick, T.
Szanto, A.
author2_role author
author
author
dc.subject.none.fl_str_mv Double-sum formula
Subresultants
Vandermonde determinant
topic Double-sum formula
Subresultants
Vandermonde determinant
dc.description.none.fl_txt_mv 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.
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.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
url http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Symb. Comput. 2007;42(3):290-297
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.623145

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