In mathematics, an algebraic function is informally a function which satisfies a polynomial equation whose coefficients are themselves polynomials. For example, an algebraic function in one variable x is a solution y for an equation where the coefficients ai(x) are polynomial functions of x. A function which is not algebraic is called a transcendental...

n abstract algebra, a field extension L/K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions which are not algebraic, i.e. which contain transcendental elements, are called transcendental. For example, the field extension R/Q, that...

In mathematics, if L is a field extension of K, then an element a of L is called an algebraic element over K, or just algebraic over K, if there exists some non-zero polynomial g(x) with coefficients in K such that g(a)=0. Elements of L which are not algebraic over K are called transcendental over K. These notions generalize the algebraic numbers...

The solution of an algebraic equation, often one that seeks zeros of a polynomial, is sometimes said to admit an "algebraic solution" or a "solution in radicals" if function that expresses the solution in terms of the coefficients relies only on addition, subtraction, multiplication, division, and the extraction of roots. The most well-known example...