algebraic function field

An algebraic function is a function f(x) which satisfies p(x, f(x)) = 0, where p(x, y) is a polynomial in x and y with integer coefficients. Functions that can be constructed using only a finite number of elementary operations together with the inverses of functions capable of being so constructed are examples of algebraic functions. Nonalgebraic functions are called transcendental functions.

algebraic equation | elementary function | elementary operation | transcendental function