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Symbolic-Numeric Factorization of Differential Operators

Factorisation Symbolique-Numérique d'Opérateurs Différentiels


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.
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Dates and versions

hal-03580658 , version 1 (18-02-2022)
hal-03580658 , version 2 (18-05-2022)
hal-03580658 , version 3 (31-05-2022)
hal-03580658 , version 4 (02-06-2022)



Frédéric Chyzak, Alexandre Goyer, Marc Mezzarobba. Symbolic-Numeric Factorization of Differential Operators. ISSAC '22, Jul 2022, Lille, France. ⟨10.1145/3476446.3535503⟩. ⟨hal-03580658v4⟩
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