On the regularity property of differential polynomials modulo regular differential chains

Authors:
François Boulier;François Lemaire;Alexandre Sedoglavic
Affiliations:
Université Lille I, LIFL, Villeneuve d'Ascq, France;Université Lille I, LIFL, Villeneuve d'Ascq, France;Université Lille I, LIFL, Villeneuve d'Ascq, France
Venue:
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Year:
2011

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Abstract

This paper provides an algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists. A regularity test for polynomials modulo regular chains is revisited in the nondifferential setting and lifted to differential algebra. A new characterization of regular chains is provided.