Bounds for algorithms in differential algebra

Abstract

We 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.

40 pages

References in corpus (1)

• Canonical Characteristic Sets of Characterizable Differential Ideals

Cited by in corpus (6)

• A Bound for Orders in Differential Nullstellensatz
• Canonical Characteristic Sets of Characterizable Differential Ideals
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• Computing Constraint Sets for Differential Fields
• Method for estimating hidden structures determined by unidentifiable state-space models and time-series data based on the Groebner basis
• Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems