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.
.. toctree:: :maxdepth: 1 sage/rings/function_field/function_field sage/rings/function_field/function_field_rational sage/rings/function_field/function_field_polymod sage/rings/function_field/element sage/rings/function_field/element_rational sage/rings/function_field/element_polymod sage/rings/function_field/order sage/rings/function_field/order_rational sage/rings/function_field/order_basis sage/rings/function_field/order_polymod sage/rings/function_field/ideal sage/rings/function_field/ideal_rational sage/rings/function_field/ideal_polymod sage/rings/function_field/place sage/rings/function_field/place_rational sage/rings/function_field/place_polymod sage/rings/function_field/divisor sage/rings/function_field/differential sage/rings/function_field/valuation_ring sage/rings/function_field/derivations sage/rings/function_field/derivations_rational sage/rings/function_field/derivations_polymod sage/rings/function_field/maps sage/rings/function_field/extensions sage/rings/function_field/constructor
A basic reference for the theory of algebraic function fields is [Stich2009]_.
.. toctree:: :maxdepth: 1 sage/rings/function_field/hermite_form_polynomial