distinct zeros of p. The monodromy group acts by permuting the factors, and thus forms the monodromy representation of the Galois group of p. (The monodromy action on the universal covering space is related but different notion in the theory of Riemann surfaces.) History The ideas surrounding algebraic functions go back at least as far as René Descartes. The first discussion of algebraic functions appears to have been in Edward Waring's 1794 An Essay on the Principles of Human Knowledge in which he writes: let a quantity denoting the ordinate, be an algebraic function of the abscissa x, by the common methods of division and extraction of roots, reduce it into an infinite series ascending or descending according to the dimensions of x, and then find the integral of each of the resulting terms. See also Algebraic expression Analytic function Complex function Elementary function Function (mathematics) Generalized function List of special functions and eponyms List of types of functions Polynomial Rational function Special functions Transcendental function References External links Definition of "Algebraic function" in the Encyclopedia of Math Definition of "Algebraic function" in David J. Darling's Internet Encyclopedia of Science Analytic functions Functions and mappings Meromorphic functions Special functions Types of functions Polynomials