Path: blob/develop/src/doc/en/reference/function_fields/index.rst
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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`. .. 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]_. Jacobians of function fields ---------------------------- Arithmetic in Jacobians of function fields are available in two flavors. .. toctree:: :maxdepth: 1 sage/rings/function_field/jacobian_base sage/rings/function_field/jacobian_hess sage/rings/function_field/jacobian_khuri_makdisi sage/rings/function_field/khuri_makdisi A Support Module ---------------- .. toctree:: :maxdepth: 1 sage/rings/function_field/hermite_form_polynomial .. include:: ../footer.txt