Further results on the computation of the annihilators of integro-differential operators

• Published in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation
• Main Authors: Cluzeau, Thomas, Pinto, Camille, Quadrat, Alban
• Other Authors: XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs (OURAGAN), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2023
• Subjects: Non-commutative operators; integro-differential operators; annihilator; coherence; [MATH]Mathematics [math]; [INFO]Computer Science [cs]; Norway; Tromso
• Online Access: https://inria.hal.science/hal-04203853; https://inria.hal.science/hal-04203853/document; https://inria.hal.science/hal-04203853/file/article_issac_publie%CC%81.pdf; https://doi.org/10.1145/3597066.3597083

International audience This paper exposes some effective aspects of the algebra of linear ordinary integro-differential operators with polynomial coefficients. More precisely, we prove that the annihilator of an evaluation operator is a finitely generated ideal which can be explicitly characterized and computed. This is an advance towards the development of an effective elimination theory for ordinary integro-differential operators and an effective study of linear systems of integro-differential equations with polynomial coefficients.