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

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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...

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Autores principales: D'Alfonso, L., Jeronimo, G., Solernó, P.
Formato: Artículo publishedVersion
Lenguaje:Inglés
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0885064X_v22_n3_p396_DAlfonso
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spelling paperaa:paper_0885064X_v22_n3_p396_DAlfonso2023-06-12T16:48:19Z On the complexity of the resolvent representation of some prime differential ideals J. Complexity 2006;22(3):396-430 D'Alfonso, L. Jeronimo, G. Solernó, P. 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 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. 2006 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
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
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AT jeronimog onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals
AT solernop onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals
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