Algebraic Function Fields#
Sage allows basic computations with elements and ideals in orders of algebraic function fields over arbitrary constant fields. Advanced computations, like computing the genus or a basis of the Riemann-Roch space of a divisor, are available for function fields over finite fields, number fields, and the algebraic closure of \(\QQ\).
- Function Fields
- Function Fields: rational
- Function Fields: extension
- Elements of function fields
- Elements of function fields: rational
- Elements of function fields: extension
- Orders of function fields
- Orders of function fields: rational
- Orders of function fields: basis
- Orders of function fields: extension
- Ideals of function fields
- Ideals of function fields: rational
- Ideals of function fields: extension
- Places of function fields
- Places of function fields: rational
- Places of function fields: extension
- Divisors of function fields
- Differentials of function fields
- Valuation rings of function fields
- Derivations of function fields
- Derivations of function fields: rational
- Derivations of function fields: extension
- Morphisms of function fields
- Special extensions of function fields
- Factories to construct function fields
A basic reference for the theory of algebraic function fields is [Stich2009].