[A generalization of the Boulier–Buchberger criterion for the computation of characteristic sets of differential ideals]
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 on the same arbitrary differential polynomial.
Nous généralisons l’analogue du premier critère de Buchberger, dû à Boulier et al., pour détecter les réductions inutiles de S-polynômes, lors des calculs d’ensembles caractéristiques d’idéaux différentiels. La version primitive suppose des polynômes linéaires ; le résultat est ici étendu à un produit de polynômes différentiels linéaires, appliqués à un même polynôme différentiel, arbitraire.
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Amir Hashemi 1; François Ollivier 2
@article{CRMATH_2022__360_G3_255_0, author = {Amir Hashemi and Fran\c{c}ois Ollivier}, title = {Une g\'en\'eralisation du crit\`ere de {Boulier{\textendash}Buchberger} pour le calcul des ensembles caract\'eristiques d{\textquoteright}id\'eaux diff\'erentiels}, journal = {Comptes Rendus. Math\'ematique}, pages = {255--264}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.295}, language = {fr}, }
TY - JOUR AU - Amir Hashemi AU - François Ollivier TI - Une généralisation du critère de Boulier–Buchberger pour le calcul des ensembles caractéristiques d’idéaux différentiels JO - Comptes Rendus. Mathématique PY - 2022 SP - 255 EP - 264 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.295 LA - fr ID - CRMATH_2022__360_G3_255_0 ER -
%0 Journal Article %A Amir Hashemi %A François Ollivier %T Une généralisation du critère de Boulier–Buchberger pour le calcul des ensembles caractéristiques d’idéaux différentiels %J Comptes Rendus. Mathématique %D 2022 %P 255-264 %V 360 %I Académie des sciences, Paris %R 10.5802/crmath.295 %G fr %F CRMATH_2022__360_G3_255_0
Amir Hashemi; François Ollivier. Une généralisation du critère de Boulier–Buchberger pour le calcul des ensembles caractéristiques d’idéaux différentiels. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 255-264. doi : 10.5802/crmath.295. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.295/
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