{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/symbolic-numeric-factorization-of","title":"Symbolic-Numeric Factorization of Differential Operators","arxiv_id":"2205.08991","date":"2022-05-18","proceeding":null,"authors":["Frédéric Chyzak","Alexandre Goyer","Marc Mezzarobba"],"abstract":"We present a symbolic-numeric Las Vegas algorithm for factoring Fuchsian ordinary differential operators with rational function coefficients. The new algorithm combines ideas of van Hoeij's \"local-to-global\" method and of the ''analytic'' approach proposed by van der Hoeven. It essentially reduces to the former in ''easy'' cases where the local-to-global method succeeds, and to an optimized variant of the latter in the \"hardest\" cases, while handling intermediate cases more efficiently than both.","url_abs":"https://arxiv.org/abs/2205.08991v3","url_pdf":"https://arxiv.org/pdf/2205.08991v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"symbolic-numeric-factorization-of","repo_url":"https://github.com/pierrevanhove/picardfuchs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}