rational function field
nounA rational function field is a math set made of fractions of polynomials.
In algebra class, we learned that the rational function field contains every fraction you can build from polynomials.
SYNONYMS
OTHER MEANINGS
2. In algebraic geometry, the field of rational functions on an irreducible variety, used to study its birational properties.
The rational function field of the curve helped the geometers classify its birational type.
3. The field of fractions of a polynomial ring over a base field, often denoted K(x).
For the base field K, the rational function field K(x) consists of quotients of polynomials in x.
4. A field generated by adjoining one or more indeterminates to a base field, forming the ambient structure for rational maps.
Adjoining the variable t to the base field produced a rational function field used to define rational maps.