  We study the problem of decomposition (non-commutative factorization) of
linear ordinary differential operators near an irregular singular point. The
solution (given in terms of the Newton diagram and the respective
characteristic numbers) is known for quite some time, though the proofs are
rather involved.
  We suggest a process of reduction of the non-commutative problem to its
commutative analog, the problem of factorization of pseudopolynomials, which is
known since Newton invented his method of rotating ruler. It turns out that
there is an "automatic translation" which allows to obtain the results for
formal factorization in the Weyl algebra from well known results in local
analytic geometry.
  Besides, we draw some (apparently unnoticed) parallelism between the formal
factorization of linear operators and formal diagonalization of systems of
linear first order differential equations.
