Closed formula for univariate subresultants in multiple roots

Autores
D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Valdettaro, Marcelo Alejandro
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials and is obtained by using multivariate symmetric interpolation via an Exchange Lemma.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
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
Fil: Valdettaro, Marcelo Alejandro. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
EXCHANGE LEMMA
FORMULAS IN ROOTS
SCHUR FUNCTIONS
SUBRESULTANTS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/117681
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/117681
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Closed formula for univariate subresultants in multiple rootsD'Andrea, CarlosKrick, Teresa Elena GenovevaSzanto, AgnesValdettaro, Marcelo AlejandroEXCHANGE LEMMAFORMULAS IN ROOTSSCHUR FUNCTIONSSUBRESULTANTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials and is obtained by using multivariate symmetric interpolation via an Exchange Lemma.Fil: D'Andrea, Carlos. Universidad de Barcelona; EspañaFil: 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 UnidosFil: Valdettaro, Marcelo Alejandro. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science Inc2019-03info: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/11336/117681D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Valdettaro, Marcelo Alejandro; Closed formula for univariate subresultants in multiple roots; Elsevier Science Inc; Linear Algebra and its Applications; 565; 3-2019; 123-1550024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2018.12.010info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0024379518305731?via%3Dihubinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1612.05160info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T10:54:57Zoai:ri.conicet.gov.ar:11336/117681instacron: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:34982025-09-17 10:54:57.629CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Closed formula for univariate subresultants in multiple roots
title Closed formula for univariate subresultants in multiple roots
spellingShingle Closed formula for univariate subresultants in multiple roots
D'Andrea, Carlos
EXCHANGE LEMMA
FORMULAS IN ROOTS
SCHUR FUNCTIONS
SUBRESULTANTS
title_short Closed formula for univariate subresultants in multiple roots
title_full Closed formula for univariate subresultants in multiple roots
title_fullStr Closed formula for univariate subresultants in multiple roots
title_full_unstemmed Closed formula for univariate subresultants in multiple roots
title_sort Closed formula for univariate subresultants in multiple roots
dc.creator.none.fl_str_mv D'Andrea, Carlos
Krick, Teresa Elena Genoveva
Szanto, Agnes
Valdettaro, Marcelo Alejandro
author D'Andrea, Carlos
author_facet D'Andrea, Carlos
Krick, Teresa Elena Genoveva
Szanto, Agnes
Valdettaro, Marcelo Alejandro
author_role author
author2 Krick, Teresa Elena Genoveva
Szanto, Agnes
Valdettaro, Marcelo Alejandro
author2_role author
author
author
dc.subject.none.fl_str_mv EXCHANGE LEMMA
FORMULAS IN ROOTS
SCHUR FUNCTIONS
SUBRESULTANTS
topic EXCHANGE LEMMA
FORMULAS IN ROOTS
SCHUR FUNCTIONS
SUBRESULTANTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials and is obtained by using multivariate symmetric interpolation via an Exchange Lemma.
Fil: D'Andrea, Carlos. Universidad de Barcelona; España
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
Fil: Valdettaro, Marcelo Alejandro. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials and is obtained by using multivariate symmetric interpolation via an Exchange Lemma.
publishDate 2019
dc.date.none.fl_str_mv 2019-03
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/11336/117681
D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Valdettaro, Marcelo Alejandro; Closed formula for univariate subresultants in multiple roots; Elsevier Science Inc; Linear Algebra and its Applications; 565; 3-2019; 123-155
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/117681
identifier_str_mv D'Andrea, Carlos; Krick, Teresa Elena Genoveva; Szanto, Agnes; Valdettaro, Marcelo Alejandro; Closed formula for univariate subresultants in multiple roots; Elsevier Science Inc; Linear Algebra and its Applications; 565; 3-2019; 123-155
0024-3795
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.laa.2018.12.010
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0024379518305731?via%3Dihub
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1612.05160
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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
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score 13.001348

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