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
• Elements of function fields
• Orders of function fields
• Ideals of function fields
• Places of function fields
• Divisors of function fields
• Differentials of function fields
• Valuation rings of function fields
• 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].

A Support Module

• Hermite form computation for function fields

Indices and Tables

• Index

• Module Index

• Search Page