Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients

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} anoth...

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Autores principales: D'Alfonso, L., Jeronimo, G., Solernó, P.
Formato: JOUR
Materias:
DAE systems
Differential algebra
Differential elimination
Differential Hilbert Nullstellensatz
Polynomials
Differential algebraic equations
Differential algebras
Differential equation systems
Differential polynomial
Hilbert
Successive derivatives
Ordinary differential equations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0885064X_v30_n5_p588_DAlfonso
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0885064X_v30_n5_p588_DAlfonso2023-10-03T15:40:41Z Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients D'Alfonso, L. Jeronimo, G. Solernó, P. DAE systems Differential algebra Differential elimination Differential Hilbert Nullstellensatz Polynomials DAE systems Differential algebraic equations Differential algebras Differential elimination Differential equation systems Differential polynomial Hilbert Successive derivatives Ordinary differential equations 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. © 2014 Elsevier Inc. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0885064X_v30_n5_p588_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 DAE systems
Differential algebra
Differential elimination
Differential Hilbert Nullstellensatz
Polynomials
DAE systems
Differential algebraic equations
Differential algebras
Differential elimination
Differential equation systems
Differential polynomial
Hilbert
Successive derivatives
Ordinary differential equations
spellingShingle DAE systems
Differential algebra
Differential elimination
Differential Hilbert Nullstellensatz
Polynomials
DAE systems
Differential algebraic equations
Differential algebras
Differential elimination
Differential equation systems
Differential polynomial
Hilbert
Successive derivatives
Ordinary differential equations
D'Alfonso, L.
Jeronimo, G.
Solernó, P.
Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
topic_facet DAE systems
Differential algebra
Differential elimination
Differential Hilbert Nullstellensatz
Polynomials
DAE systems
Differential algebraic equations
Differential algebras
Differential elimination
Differential equation systems
Differential polynomial
Hilbert
Successive derivatives
Ordinary differential equations
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. © 2014 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 Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
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
url http://hdl.handle.net/20.500.12110/paper_0885064X_v30_n5_p588_DAlfonso
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AT jeronimog effectivedifferentialnullstellensatzforordinarydaesystemswithconstantcoefficients
AT solernop effectivedifferentialnullstellensatzforordinarydaesystemswithconstantcoefficients
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