rational function

A real function R(x) of a single variable x is called if it can be written as a quotient


where P(x) and Q(x) are polynomialsMathworldPlanetmathPlanetmathPlanetmath in x with real coefficients. When one is only interested in algebraicMathworldPlanetmath properties of R(x) or P(x) and Q(x), it is convenient to forget that they define functions and simply treat them as algebraic expressions in x. In this case R(x) is referred to as a rational expression.

In general, a rational function (expression) R(x1,,xn) has the form


where P(x1,,xn) and Q(x1,,xn) are polynomials in the variables (x1,,xn) with coefficients in some field or ring S.

In this sense, R(x1,,xn) can be regarded as an element of the fraction field S(x1,,xn) of the polynomial ring S[x1,,xn].

Title rational function
Canonical name RationalFunction
Date of creation 2013-03-22 13:38:54
Last modified on 2013-03-22 13:38:54
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 26C15
Synonym rational expression
Related topic PolynomialRing
Related topic FractionField
Related topic RealFunction
Related topic PropertiesOfEntireFunctions
Related topic IntegrationOfFractionPowerExpressions