algebraic function field
nounA special math set where you can add, subtract, multiply, and divide fractions made from letters and numbers.
In class, we learned that an algebraic function field is built from fractions of polynomials.
OTHER MEANINGS
2. A field made by adjoining a transcendental element to a base field and then taking the algebraic closure inside a finite extension.
The algebraic function field of the curve was studied over the complex numbers.
3. In algebraic geometry, the field of rational functions on an algebraic variety.
The function field of a smooth projective curve determines the curve up to isomorphism.
4. A finitely generated field extension of transcendence degree one over a base field.
Every algebraic function field in one variable over a finite field has a zeta function.