Une g\'{e}n\'{e}ralisation du crit\`{e}re de Boulier -- Buchberger pour le calcul des ensembles caract\'{e}ristiques d'id\'{e}aux diff\'{e}rentiels

TL;DR

This paper extends Buchberger's criterion for differential ideals, enabling more efficient computation of characteristic sets by identifying unnecessary reductions involving products of linear differential polynomials.

Contribution

It generalizes Boulier et al.'s criterion from linear polynomials to products of linear differential polynomials depending on the same arbitrary differential polynomial.

Findings

Extended Buchberger's criterion to broader class of differential polynomials

Improved efficiency in computing characteristic sets of differential ideals

Provides theoretical foundation for optimized differential algebra algorithms

Abstract

We generalize the analog of Buchberger's first criterion, stated by Boulier et al., for detecting useless S-polynomials reductions in the computation of characteristic sets of differential ideals. The original version assumes linear polynomials; this result is here extended to a product of linear differential polynomials depending of the same arbitrary differential polynomial.