  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.
