Bounds for algorithms in differential algebra

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dc.creatorGolubitsky, Oleg
dc.creatorKondratieva, Marina
dc.creatorMaza, Marc Moreno
dc.creatorOvchinnikov, Alexey
dc.date2007-02-16
dc.date.accessioned2026-07-07T12:45:57Z
dc.date.available2026-07-07T12:45:57Z
dc.descriptionWe consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F, let M(F) be the sum of maximal orders of differential indeterminates occurring in F. We propose a modification of the Rosenfeld-Groebner algorithm, in which for every intermediate polynomial system F, the bound M(F) is less than or equal to (n-1)!M(G), where G is the initial set of generators of the radical ideal. In particular, the resulting regular systems satisfy the bound. Since regular ideals can be decomposed into characterizable components algebraically, the bound also holds for the orders of derivatives occurring in a characteristic decomposition of a radical differential ideal. We also give an algorithm for converting a characteristic decomposition of a radical differential ideal from one ranking into another. This algorithm performs all differentiations in the beginning and then uses a purely algebraic decomposition algorithm.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/math/0702470
dc.identifierhttp://arxiv.org/abs/math/0702470
dc.identifierJournal of Symbolic Computation 43 (8) (2008) 582-610
dc.identifierdoi:10.1016/j.jsc.2007.12.002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221222
dc.subjectCommutative Algebra
dc.subject12H05; 13N10; 13P10
dc.titleBounds for algorithms in differential algebra
dc.typetext

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