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# 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].

## Jacobians of function fields

Arithmetic in Jacobians of function fields are available in two flavors.

- Jacobians of function fields
- Jacobians in Hess model
- Jacobians in Khuri-Makdisi model
- Khuri-Makdisi algorithms for arithmetic in Jacobians

## A Support Module

- Hermite form computation for function fields

# Indices and Tables

- Index

- Module Index

- Search Page