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Abstract:

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.

Registro:

Documento: Artículo
Título:Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients
Autor:D'Alfonso, L.; Jeronimo, G.; Solernó, P.
Filiación:Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
Departamento de Matemática and IMAS, UBA-CONICET, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
Palabras clave: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
Año:2014
Volumen:30
Número:5
Página de inicio:588
Página de fin:603
DOI: http://dx.doi.org/10.1016/j.jco.2014.01.001
Título revista:Journal of Complexity
Título revista abreviado:J. Complexity
ISSN:0885064X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0885064X_v30_n5_p588_DAlfonso

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Citas:

---------- APA ----------
D'Alfonso, L., Jeronimo, G. & Solernó, P. (2014) . Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients. Journal of Complexity, 30(5), 588-603.
http://dx.doi.org/10.1016/j.jco.2014.01.001
---------- CHICAGO ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. "Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients" . Journal of Complexity 30, no. 5 (2014) : 588-603.
http://dx.doi.org/10.1016/j.jco.2014.01.001
---------- MLA ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. "Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients" . Journal of Complexity, vol. 30, no. 5, 2014, pp. 588-603.
http://dx.doi.org/10.1016/j.jco.2014.01.001
---------- VANCOUVER ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. Effective differential Nullstellensatz for ordinary DAE systems with constant coefficients. J. Complexity. 2014;30(5):588-603.
http://dx.doi.org/10.1016/j.jco.2014.01.001