Rational function
Ratio of polynomial functions / From Wikipedia, the free encyclopedia
For the use in automata theory, see Finite-state transducer. For the use in monoid theory, see Rational function (monoid).
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L.
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The set of rational functions over a field K is a field, the field of fractions of the ring of the polynomial functions over K.