Bounds and algebraic algorithms in differential algebra: the ordinary case
Consider the Rosenfeld-Groebner algorithm for computing a regular
decomposition of a radical differential ideal generated by a set
of ordinary differential polynomials. This algorithm inputs a
system of differential polynomials and a
ranking on derivatives and constructs finitely many regular systems
equivalent to the original one. The property of
regularity allows to check consistency of the systems and
membership to the corresponding differential ideals.
We propose a bound on the orders of derivatives
occurring in all intermediate and final systems computed by the
Rosenfeld-Groebner algorithm and outline its proof.
We also reduce the problem of conversion of
a regular decomposition of a radical
differential ideal from one ranking to another to a purely
algebraic problem.
Differential algebra
Rosenfeld Groebner Algorithm
1-9
Regular Paper
Marc
Moreno Maza
Marc Moreno Maza
Oleg
Golubitsky
Oleg Golubitsky
Marina V.
Kondratieva
Marina V. Kondratieva
Alexey
Ovchinnikov
Alexey Ovchinnikov
10.4230/DagSemProc.06271.4
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode