On the complexity of the resolvent representation of some prime differential ideals

Autores
D'Alfonso, L.; Jeronimo, G.; Solernó, P.
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. © 2005 Elsevier Inc. All rights reserved.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Complexity 2006;22(3):396-430
Materia
Differential algebra
Differential Hilbert function
Elimination theory
Probabilistic algorithms
Resolvent representation
Straight-line programs
Algorithms
Computation theory
Differential equations
Functions
Polynomials
Probabilistic logics
Differential algebra
Differential Hilbert function
Elimination theory
Resolvent representation
Straight-line programs
Computational complexity
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_0885064X_v22_n3_p396_DAlfonso
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oai_identifier_str paperaa:paper_0885064X_v22_n3_p396_DAlfonso
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling On the complexity of the resolvent representation of some prime differential idealsD'Alfonso, L.Jeronimo, G.Solernó, P.Differential algebraDifferential Hilbert functionElimination theoryProbabilistic algorithmsResolvent representationStraight-line programsAlgorithmsComputation theoryDifferential equationsFunctionsPolynomialsProbabilistic logicsDifferential algebraDifferential Hilbert functionElimination theoryResolvent representationStraight-line programsComputational complexityWe prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. © 2005 Elsevier Inc. All rights reserved.Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2006info: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_0885064X_v22_n3_p396_DAlfonsoJ. Complexity 2006;22(3):396-430reponame: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/ar2025-11-06T09:39:57Zpaperaa:paper_0885064X_v22_n3_p396_DAlfonsoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-11-06 09:39:59.132Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv On the complexity of the resolvent representation of some prime differential ideals
title On the complexity of the resolvent representation of some prime differential ideals
spellingShingle On the complexity of the resolvent representation of some prime differential ideals
D'Alfonso, L.
Differential algebra
Differential Hilbert function
Elimination theory
Probabilistic algorithms
Resolvent representation
Straight-line programs
Algorithms
Computation theory
Differential equations
Functions
Polynomials
Probabilistic logics
Differential algebra
Differential Hilbert function
Elimination theory
Resolvent representation
Straight-line programs
Computational complexity
title_short On the complexity of the resolvent representation of some prime differential ideals
title_full On the complexity of the resolvent representation of some prime differential ideals
title_fullStr On the complexity of the resolvent representation of some prime differential ideals
title_full_unstemmed On the complexity of the resolvent representation of some prime differential ideals
title_sort On the complexity of the resolvent representation of some prime differential ideals
dc.creator.none.fl_str_mv D'Alfonso, L.
Jeronimo, G.
Solernó, P.
author D'Alfonso, L.
author_facet D'Alfonso, L.
Jeronimo, G.
Solernó, P.
author_role author
author2 Jeronimo, G.
Solernó, P.
author2_role author
author
dc.subject.none.fl_str_mv Differential algebra
Differential Hilbert function
Elimination theory
Probabilistic algorithms
Resolvent representation
Straight-line programs
Algorithms
Computation theory
Differential equations
Functions
Polynomials
Probabilistic logics
Differential algebra
Differential Hilbert function
Elimination theory
Resolvent representation
Straight-line programs
Computational complexity
topic Differential algebra
Differential Hilbert function
Elimination theory
Probabilistic algorithms
Resolvent representation
Straight-line programs
Algorithms
Computation theory
Differential equations
Functions
Polynomials
Probabilistic logics
Differential algebra
Differential Hilbert function
Elimination theory
Resolvent representation
Straight-line programs
Computational complexity
dc.description.none.fl_txt_mv We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. © 2005 Elsevier Inc. All rights reserved.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. © 2005 Elsevier Inc. All rights reserved.
publishDate 2006
dc.date.none.fl_str_mv 2006
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_0885064X_v22_n3_p396_DAlfonso
url http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso
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. Complexity 2006;22(3):396-430
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 12.976206

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