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: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0885064X_v30_n5_p588_DAlfonso |
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| Sumario: | 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. |
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