Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients

Autores
D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, f a finite family of differential polynomials in the ring K{x} and fεK{x} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing K. Let d max{deg(f),deg(f)} and max{2,ord(f),ord(f)}. We show that fM belongs to the algebraic ideal generated by the successive derivatives of f of order at most L=(nd)2c(n)3, for a suitable universal constant c>0, and M=dn(+L+1). The previously known bounds for L and M are not elementary recursive.
Fil: Lisi D'Alfonso. Universidad de Buenos Aires. Ciclo Básico Común; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pablo Solernó. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
DAE SYSTEMS
DIFFERENTIAL ALGEBRA
DIFFERENTIAL ELIMINATION
DIFFERENTIAL HILBERT NULLSTELLENSATZ
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:11336/93869
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/93869
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Effective differential Nullstellensatz for ordinary DAE systems with constant coefficientsD'Alfonso, LisiJeronimo, Gabriela TaliSolernó, Pablo LuisDAE SYSTEMSDIFFERENTIAL ALGEBRADIFFERENTIAL ELIMINATIONDIFFERENTIAL HILBERT NULLSTELLENSATZhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, f a finite family of differential polynomials in the ring K{x} and fεK{x} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing K. Let d max{deg(f),deg(f)} and max{2,ord(f),ord(f)}. We show that fM belongs to the algebraic ideal generated by the successive derivatives of f of order at most L=(nd)2c(n)3, for a suitable universal constant c>0, and M=dn(+L+1). The previously known bounds for L and M are not elementary recursive.Fil: Lisi D'Alfonso. Universidad de Buenos Aires. Ciclo Básico Común; ArgentinaFil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Pablo Solernó. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAcademic Press Inc Elsevier Science2014-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93869D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 5; 10-2014; 588-6030885-064XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2014.01.001info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X14000028info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:08:30Zoai:ri.conicet.gov.ar:11336/93869instacron: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:34982025-09-10 13:08:30.899CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
title Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
spellingShingle Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
D'Alfonso, Lisi
DAE SYSTEMS
DIFFERENTIAL ALGEBRA
DIFFERENTIAL ELIMINATION
DIFFERENTIAL HILBERT NULLSTELLENSATZ
title_short Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
title_full Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
title_fullStr Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
title_full_unstemmed Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
title_sort Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
dc.creator.none.fl_str_mv D'Alfonso, Lisi
Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author D'Alfonso, Lisi
author_facet D'Alfonso, Lisi
Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author_role author
author2 Jeronimo, Gabriela Tali
Solernó, Pablo Luis
author2_role author
author
dc.subject.none.fl_str_mv DAE SYSTEMS
DIFFERENTIAL ALGEBRA
DIFFERENTIAL ELIMINATION
DIFFERENTIAL HILBERT NULLSTELLENSATZ
topic DAE SYSTEMS
DIFFERENTIAL ALGEBRA
DIFFERENTIAL ELIMINATION
DIFFERENTIAL HILBERT NULLSTELLENSATZ
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 give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, f a finite family of differential polynomials in the ring K{x} and fεK{x} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing K. Let d max{deg(f),deg(f)} and max{2,ord(f),ord(f)}. We show that fM belongs to the algebraic ideal generated by the successive derivatives of f of order at most L=(nd)2c(n)3, for a suitable universal constant c>0, and M=dn(+L+1). The previously known bounds for L and M are not elementary recursive.
Fil: Lisi D'Alfonso. Universidad de Buenos Aires. Ciclo Básico Común; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pablo Solernó. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, f a finite family of differential polynomials in the ring K{x} and fεK{x} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing K. Let d max{deg(f),deg(f)} and max{2,ord(f),ord(f)}. We show that fM belongs to the algebraic ideal generated by the successive derivatives of f of order at most L=(nd)2c(n)3, for a suitable universal constant c>0, and M=dn(+L+1). The previously known bounds for L and M are not elementary recursive.
publishDate 2014
dc.date.none.fl_str_mv 2014-10
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/11336/93869
D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 5; 10-2014; 588-603
0885-064X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93869
identifier_str_mv D'Alfonso, Lisi; Jeronimo, Gabriela Tali; Solernó, Pablo Luis; Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients; Academic Press Inc Elsevier Science; Journal Of Complexity; 30; 5; 10-2014; 588-603
0885-064X
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.jco.2014.01.001
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0885064X14000028
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 12.993085

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