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”法和范德霍芬提出的“分析”法。 在“地方到全球”法成功的情况下,新算法基本上减少了前者的“容易”法,在“最困难”的情况下,也减少了后者的优化变式,同时比两者都更高效地处理中间案件。