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

Mostrar todas las versiones(3)

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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	D'Alfonso, L., Jeronimo, G., Solernó, P.
Formato:	Artículo publishedVersion
Publicado:	2006
Materias:	Differential algebra Differential Hilbert function Elimination theory Probabilistic algorithms Resolvent representation Straight-line programs Algorithms Computation theory Differential equations Functions Polynomials Probabilistic logics Computational complexity
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v22_n3_p396_DAlfonso_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_0885064X_v22_n3_p396_DAlfonso_oai
record_format	dspace
spelling	I28-R145-paper_0885064X_v22_n3_p396_DAlfonso_oai2024-08-16 D'Alfonso, L. Jeronimo, G. Solernó, P. 2006 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Complexity 2006;22(3):396-430 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 On the complexity of the resolvent representation of some prime differential ideals info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v22_n3_p396_DAlfonso_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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
spellingShingle	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 D'Alfonso, L. Jeronimo, G. Solernó, P. On the complexity of the resolvent representation of some prime differential ideals
topic_facet	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
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.
format	Artículo Artículo publishedVersion
author	D'Alfonso, L. Jeronimo, G. Solernó, P.
author_facet	D'Alfonso, L. Jeronimo, G. Solernó, P.
author_sort	D'Alfonso, L.
title	On the complexity of the resolvent representation of some prime differential ideals
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
publishDate	2006
url	http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v22_n3_p396_DAlfonso_oai
work_keys_str_mv	AT dalfonsol onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals AT jeronimog onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals AT solernop onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals
_version_	1809357102237351936

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

Ejemplares similares