Index

B

base_field() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

basis() (sage.rings.function_field.function_field_order.FunctionFieldOrder_basis method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_rational method)

C

characteristic() (sage.rings.function_field.function_field.FunctionField method) characteristic_polynomial() (sage.rings.function_field.function_field_element.FunctionFieldElement method) charpoly() (sage.rings.function_field.function_field_element.FunctionFieldElement method) codomain() (sage.rings.function_field.maps.MapFunctionFieldToVectorSpace method) (sage.rings.function_field.maps.MapVectorSpaceToFunctionField method)

constant_base_field() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method) constant_field() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method) create_key() (sage.rings.function_field.constructor.FunctionFieldFactory method) (sage.rings.function_field.constructor.FunctionFieldPolymodFactory method) create_object() (sage.rings.function_field.constructor.FunctionFieldFactory method) (sage.rings.function_field.constructor.FunctionFieldPolymodFactory method)

D

degree() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method) denominator() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method)

derivation() (sage.rings.function_field.function_field.RationalFunctionField method) domain() (sage.rings.function_field.maps.MapFunctionFieldToVectorSpace method) (sage.rings.function_field.maps.MapVectorSpaceToFunctionField method)

E

element() (sage.rings.function_field.function_field_element.FunctionFieldElement_polymod method) (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method) equation_order() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

extension() (sage.rings.function_field.function_field.FunctionField method)

F

factor() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method) field() (sage.rings.function_field.function_field.RationalFunctionField method) fraction_field() (sage.rings.function_field.function_field_order.FunctionFieldOrder method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_basis method) free_module() (sage.rings.function_field.function_field_order.FunctionFieldOrder_basis method) function_field() (sage.rings.function_field.function_field_order.FunctionFieldOrder method) FunctionField (class in sage.rings.function_field.function_field) FunctionField_polymod (class in sage.rings.function_field.function_field) FunctionFieldDerivation (class in sage.rings.function_field.maps) FunctionFieldDerivation_rational (class in sage.rings.function_field.maps) FunctionFieldElement (class in sage.rings.function_field.function_field_element) FunctionFieldElement_polymod (class in sage.rings.function_field.function_field_element) FunctionFieldElement_rational (class in sage.rings.function_field.function_field_element)

FunctionFieldFactory (class in sage.rings.function_field.constructor) FunctionFieldIdeal (class in sage.rings.function_field.function_field_ideal) FunctionFieldIdeal_module (class in sage.rings.function_field.function_field_ideal) FunctionFieldIsomorphism (class in sage.rings.function_field.maps) FunctionFieldMorphism (class in sage.rings.function_field.maps) FunctionFieldMorphism_polymod (class in sage.rings.function_field.maps) FunctionFieldMorphism_rational (class in sage.rings.function_field.maps) FunctionFieldOrder (class in sage.rings.function_field.function_field_order) FunctionFieldOrder_basis (class in sage.rings.function_field.function_field_order) FunctionFieldOrder_rational (class in sage.rings.function_field.function_field_order) FunctionFieldPolymodFactory (class in sage.rings.function_field.constructor)

G

gen() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_rational method)

genus() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

H

hom() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

I

ideal() (sage.rings.function_field.function_field_order.FunctionFieldOrder method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_rational method) ideal_with_gens() (in module sage.rings.function_field.function_field_ideal) ideal_with_gens_over_base() (in module sage.rings.function_field.function_field_ideal) (sage.rings.function_field.function_field_order.FunctionFieldOrder method) intersection() (sage.rings.function_field.function_field_ideal.FunctionFieldIdeal_module method) inverse_mod() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method) is_field() (sage.rings.function_field.function_field_order.FunctionFieldOrder method) is_finite() (sage.rings.function_field.function_field.FunctionField method) (sage.rings.function_field.function_field_order.FunctionFieldOrder method) is_FunctionField() (in module sage.rings.function_field.function_field)

is_FunctionFieldElement() (in module sage.rings.function_field.function_field_element) is_injective() (sage.rings.function_field.maps.FunctionFieldDerivation method) (sage.rings.function_field.maps.FunctionFieldIsomorphism method) (sage.rings.function_field.maps.FunctionFieldMorphism method) is_integral() (sage.rings.function_field.function_field_element.FunctionFieldElement method) is_noetherian() (sage.rings.function_field.function_field_order.FunctionFieldOrder method) is_perfect() (sage.rings.function_field.function_field.FunctionField method) is_RationalFunctionField() (in module sage.rings.function_field.function_field) is_square() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method) is_surjective() (sage.rings.function_field.maps.FunctionFieldIsomorphism method)

L

list() (sage.rings.function_field.function_field_element.FunctionFieldElement_polymod method) (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method)

M

make_FunctionFieldElement() (in module sage.rings.function_field.function_field_element) MapFunctionFieldToVectorSpace (class in sage.rings.function_field.maps) MapVectorSpaceToFunctionField (class in sage.rings.function_field.maps) matrix() (sage.rings.function_field.function_field_element.FunctionFieldElement method) maximal_order() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

minimal_polynomial() (sage.rings.function_field.function_field_element.FunctionFieldElement method) minpoly() (sage.rings.function_field.function_field_element.FunctionFieldElement method) module() (sage.rings.function_field.function_field_ideal.FunctionFieldIdeal_module method) monic_integral_model() (sage.rings.function_field.function_field.FunctionField_polymod method)

N

ngens() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_rational method) norm() (sage.rings.function_field.function_field_element.FunctionFieldElement method)

numerator() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method)

O

order() (sage.rings.function_field.function_field.FunctionField method)

order_with_basis() (sage.rings.function_field.function_field.FunctionField method)

P

polynomial() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field_order.FunctionFieldOrder_basis method)

polynomial_ring() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

R

random_element() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)

RationalFunctionField (class in sage.rings.function_field.function_field)

S

sage.rings.function_field.constructor (module) sage.rings.function_field.function_field (module) sage.rings.function_field.function_field_element (module) sage.rings.function_field.function_field_ideal (module)

sage.rings.function_field.function_field_order (module) sage.rings.function_field.maps (module) some_elements() (sage.rings.function_field.function_field.FunctionField method) sqrt() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method)

T

trace() (sage.rings.function_field.function_field_element.FunctionFieldElement method)

V

valuation() (sage.rings.function_field.function_field_element.FunctionFieldElement_rational method)

vector_space() (sage.rings.function_field.function_field.FunctionField_polymod method) (sage.rings.function_field.function_field.RationalFunctionField method)