  We give explicit definitions of the Weierstrass elliptic functions $\wp$ and
$\zeta$ in terms of pfaffian functions, with complexity independent of the
lattice involved. We also give such a definition for a modification of the
Weierstrass function $\sigma$. As immediate applications, we give an explicit
uniform zero estimate for $\wp$ and answer a question of Corvaja, Masser and
Zannier on additive extensions of elliptic curves.
