Definition:Algebraic Function/Real

Definition
Let $y$ be a solution to the polynomial equation:


 * $\map {p_0} x + \map {p_1} x y + \dotsb + \map {p_{n - 1} } x y^{n - 1} + \map {p_n} x y^n = 0$

where $\map {p_0} x \ne 0, \map {p_1} x, \dotsc, \map {p_n} x$ are real polynomial functions in $x$.

Then $y = \map f x$ is a (real) algebraic function:

Also see

 * Definition:Complex Algebraic Function