From a mathematical point of view, a polynomial is firstly a formal expression, and only secondly a function (on some given domain). Despite the name, the same is equally true of rational functions. In abstract algebra a definition of rational function is given as element of the fraction field of a polynomial ring. For this definition to succeed, we must start with an integral domain R (for example, a field). Then R[X,Y,..., T], the ring of polynomials in some indeterminates X, ... , T, will also be an integral domain; and we can properly take a fraction field. (In greater generality for commutative rings the construction will be a localization of a polynomial ring.)