An elementary proof of Sylvester's double sums for subresultants

Autores
D'Andrea, Carlos; Hong, Hoon; Krick, Teresa Elena Genoveva; Szanto, Agnes
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.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
Fil: Hong, Hoon. North Carolina State University; Estados Unidos
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
Materia
DOUBLE-SUM FORMULA
SUBRESULTANTS
VANDERMONDE DETERMINANT
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/127514
Acceder
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network_name_str CONICET Digital (CONICET)
spelling An elementary proof of Sylvester's double sums for subresultantsD'Andrea, CarlosHong, HoonKrick, Teresa Elena GenovevaSzanto, AgnesDOUBLE-SUM FORMULASUBRESULTANTSVANDERMONDE DETERMINANThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 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.Fil: D'Andrea, Carlos. Universidad de Barcelona; EspañaFil: Hong, Hoon. North Carolina State University; Estados UnidosFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Szanto, Agnes. North Carolina State University; Estados UnidosAcademic Press Ltd - Elsevier Science Ltd2007-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/127514D'Andrea, Carlos; Hong, Hoon; Krick, Teresa Elena Genoveva; Szanto, Agnes; An elementary proof of Sylvester's double sums for subresultants; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 42; 3; 3-2007; 290-2970747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2006.09.003info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717106000897info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604418info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:49:03Zoai:ri.conicet.gov.ar:11336/127514instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:49:04.133CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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, Carlos
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, Carlos
Hong, Hoon
Krick, Teresa Elena Genoveva
Szanto, Agnes
author D'Andrea, Carlos
author_facet D'Andrea, Carlos
Hong, Hoon
Krick, Teresa Elena Genoveva
Szanto, Agnes
author_role author
author2 Hong, Hoon
Krick, Teresa Elena Genoveva
Szanto, Agnes
author2_role author
author
author
dc.subject.none.fl_str_mv DOUBLE-SUM FORMULA
SUBRESULTANTS
VANDERMONDE DETERMINANT
topic DOUBLE-SUM FORMULA
SUBRESULTANTS
VANDERMONDE DETERMINANT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
Fil: Hong, Hoon. North Carolina State University; Estados Unidos
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
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.
publishDate 2007
dc.date.none.fl_str_mv 2007-03
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/11336/127514
D'Andrea, Carlos; Hong, Hoon; Krick, Teresa Elena Genoveva; Szanto, Agnes; An elementary proof of Sylvester's double sums for subresultants; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 42; 3; 3-2007; 290-297
0747-7171
CONICET Digital
CONICET
url http://hdl.handle.net/11336/127514
identifier_str_mv D'Andrea, Carlos; Hong, Hoon; Krick, Teresa Elena Genoveva; Szanto, Agnes; An elementary proof of Sylvester's double sums for subresultants; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 42; 3; 3-2007; 290-297
0747-7171
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2006.09.003
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717106000897
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604418
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842268951175757824
score 13.13397

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