2013/05/27 by Lisi D'Alfonso, Lisi D’Alfonso, Gabriela Jeronimo +4
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC #math.AC
paper · pdf · doi:10.48550/arxiv.1305.6298
openalex publication_date 2013/05/27 · arxiv created 2014/01/13 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 f∈ K\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\°(f), °(f)\ and ε:=max\2,\rmord(f), \rmord(f)\. We show that fM belongs to the algebraic ideal generated by the successive derivatives of f of order at most L = (nεd)^2c(nε)3, for a suitable universal constant c>0, and M=dn(ε+L+1). The previously known bounds for L and M are not elementary recursive.