Definition:Algebraic Function/Complex

Definition
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:

Also see

 * Definition:Real Algebraic Function