  We present a constructive criterion for flatness of a morphism of analytic
spaces X -> Y or, more generally, for flatness over Y of a coherent sheaf of
modules on X. The criterion is a combination of a simple linear-algebra
condition "in codimension zero" and a condition "in codimension one" which can
be used together with the Weierstrass preparation theorem to inductively reduce
the fibre dimension of the morphism.
