\begin{definition}[Definition:Algebraic Function/Complex]
Let $w$ be a solution to the polynomial equation:
:$\map {p_0} z + \map {p_1} z w + \dotsb + \map {p_{n - 1} } z w^{n - 1} + \map {p_n} z w^n = 0$
where $\map {p_0} z \ne 0, \map {p_1} z, \dotsc, \map {p_n} z$ are complex polynomial functions in $z$.
Then $w = \map f z$ is a '''(complex) algebraic function''':
\end{definition}