eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2007-05-21
1
9
10.4230/DagSemProc.06271.4
article
Bounds and algebraic algorithms in differential algebra: the ordinary case
Moreno Maza, Marc
Golubitsky, Oleg
Kondratieva, Marina V.
Ovchinnikov, Alexey
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol06271/DagSemProc.06271.4/DagSemProc.06271.4.pdf
Differential algebra
Rosenfeld Groebner Algorithm