\begin{definition}[Definition:Elliptic Function]
Let $\ds \map y x = \int_0^x \dfrac {\d t} {\sqrt {\map P t} }$ be an elliptic integral, where $\map P t$ is a polynomial of degree $3$ or $4$.
Consider the inverse of $\map y x$:
:$x = \map \phi y$
Then $\phi$ is an '''elliptic function'''.
\end{definition}