  While it is trivial to multiply two C-finite sequences (just like integers),
it is not quite so trivial to "factorize" them, or to decide whether they are
"prime". The former is plain linear algebra, while the latter is heavy-duty
non-linear algebra, getting hairy systems of algebraic equations that can be
solved, in principle, using Gr\"obner bases and the Buchberger algorithm, but,
alas, sooner or later it becomes too hard even for the fastest and largest
computers.
  The main technical novely of this article is a fast "algorithm" (it cheats
and uses floating-point arithmetic, please don't tell anyone!) for deciding
whether a given C-finite sequence can be written as a product of C-finite
sequences of lower order.
  This article accompanies the Maple package Cfinite available from
http://www.math.rutgers.edu/~zeilberg/tokhniot/Cfinite .
