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.
翻译:新的算法结合了范霍艾的“本地到全球”法和范德尔霍芬提出的“分析”法。 在“容易”法成功的情况下,新算法基本上可以降低到前者,在“最困难”的情况下,在“最困难”的情况下,可以降低到后者的优化变式,同时比两者都更高效地处理中间案件。