The classical Weierstrass preparation theorem and division theorem are a key tool in analytic geometry. They have been used by Van den Dries in his deep work on real subanalytic sets and in establishing new o-minimal structures.
Given an o-minimal structure expanding the field of reals, we show a piecewise Weierstrass preparation theorem and a piecewise Weierstrass division theorem for the ring of definable holomorphic functions. The numbers of pieces needed are determined by geometric terms. In the semialgebraic setting and for the structure of globally subanalytic sets and functions we can translate the results to the real analytic setting. As an application we show a definable global Nullstellensatz for principal ideals.