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:	JOUR
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

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spelling	todo:paper_0885064X_v22_n3_p396_DAlfonso2023-10-03T15:40:38Z On the complexity of the resolvent representation of some prime differential ideals 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. JOUR 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)
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	JOUR
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
url	http://hdl.handle.net/20.500.12110/paper_0885064X_v22_n3_p396_DAlfonso
work_keys_str_mv	AT dalfonsol onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals AT jeronimog onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals AT solernop onthecomplexityoftheresolventrepresentationofsomeprimedifferentialideals
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On the complexity of the resolvent representation of some prime differential ideals

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