Sylvester's double sums: An inductive proof of the general case

Autores
Krick, Teresa Elena Genoveva; Szanto, Agnes
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D’Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A. Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester’s double-sums.
Fil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
Materia
Subresultants
Double-Sum Formula
Induction
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:11336/14934
Acceder
id CONICETDig_5cec3af0b1c5af057f0ec3ac7fbf3f5b
oai_identifier_str oai:ri.conicet.gov.ar:11336/14934
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sylvester's double sums: An inductive proof of the general caseKrick, Teresa Elena GenovevaSzanto, AgnesSubresultantsDouble-Sum FormulaInductionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D’Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A. Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester’s double-sums.Fil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Szanto, Agnes. North Carolina State University; Estados UnidosElsevier2012-01-30info: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/11336/14934Krick, Teresa Elena Genoveva; Szanto, Agnes; Sylvester's double sums: An inductive proof of the general case; Elsevier; Journal Of Symbolic Computation; 47; 8; 30-1-2012; 942-9530747-7171enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717112000041info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2012.01.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:16Zoai:ri.conicet.gov.ar:11336/14934instacron: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 09:55:16.607CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sylvester's double sums: An inductive proof of the general case
title Sylvester's double sums: An inductive proof of the general case
spellingShingle Sylvester's double sums: An inductive proof of the general case
Krick, Teresa Elena Genoveva
Subresultants
Double-Sum Formula
Induction
title_short Sylvester's double sums: An inductive proof of the general case
title_full Sylvester's double sums: An inductive proof of the general case
title_fullStr Sylvester's double sums: An inductive proof of the general case
title_full_unstemmed Sylvester's double sums: An inductive proof of the general case
title_sort Sylvester's double sums: An inductive proof of the general case
dc.creator.none.fl_str_mv Krick, Teresa Elena Genoveva
Szanto, Agnes
author Krick, Teresa Elena Genoveva
author_facet Krick, Teresa Elena Genoveva
Szanto, Agnes
author_role author
author2 Szanto, Agnes
author2_role author
dc.subject.none.fl_str_mv Subresultants
Double-Sum Formula
Induction
topic Subresultants
Double-Sum Formula
Induction
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 introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D’Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A. Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester’s double-sums.
Fil: Krick, Teresa Elena Genoveva. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Szanto, Agnes. North Carolina State University; Estados Unidos
description In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D’Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A. Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester’s double-sums.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-30
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/11336/14934
Krick, Teresa Elena Genoveva; Szanto, Agnes; Sylvester's double sums: An inductive proof of the general case; Elsevier; Journal Of Symbolic Computation; 47; 8; 30-1-2012; 942-953
0747-7171
url http://hdl.handle.net/11336/14934
identifier_str_mv Krick, Teresa Elena Genoveva; Szanto, Agnes; Sylvester's double sums: An inductive proof of the general case; Elsevier; Journal Of Symbolic Computation; 47; 8; 30-1-2012; 942-953
0747-7171
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717112000041
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2012.01.003
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 Elsevier
publisher.none.fl_str_mv Elsevier
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_ 1842269334393585664
score 13.13397

Publicaciones similares