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rational function
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Wikidata facts
- Subclass of
- meromorphic function
- Image
- RationalDegree3.svg
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- Commons category
- Rational functions
- topic's main category
- Category:Rational functions
- studied by
- algebraic geometry
- maintained by WikiProject
- WikiProject Mathematics
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Encyclopedic overview
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.
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.
Excerpted from Wikipedia’s “rational function” article, available under the CC BY-SA 4.0 licence.