Index

A | B | C | D | E | F | G | H | I | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z

A

abs() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
abs_hom() (sage.rings.number_field.morphism.RelativeNumberFieldHomomorphism_from_abs method)
abs_non_arch() (sage.rings.number_field.number_field_element.NumberFieldElement method)
absolute_base_field() (sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_charpoly() (sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
(sage.rings.number_field.number_field_element.OrderElement_relative method)
absolute_degree() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.Order method)
absolute_different() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_discriminant() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.AbsoluteOrder method)
(sage.rings.number_field.order.RelativeOrder method)
absolute_field() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_generator() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_ideal() (sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
absolute_minpoly() (sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
(sage.rings.number_field.number_field_element.OrderElement_relative method)
absolute_norm() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
absolute_order() (sage.rings.number_field.order.AbsoluteOrder method)
(sage.rings.number_field.order.RelativeOrder method)
absolute_order_from_module_generators() (in module sage.rings.number_field.order)
absolute_order_from_ring_generators() (in module sage.rings.number_field.order)
absolute_polynomial() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_polynomial_ntl() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
absolute_ramification_index() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
absolute_vector_space() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
AbsoluteFromRelative (class in sage.rings.number_field.structure)
AbsoluteOrder (class in sage.rings.number_field.order)
additive_order() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
algebraic_closure() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
AlgebraicField (class in sage.rings.qqbar)
AlgebraicField_common (class in sage.rings.qqbar)
AlgebraicGenerator (class in sage.rings.qqbar)
AlgebraicGeneratorRelation (class in sage.rings.qqbar)
AlgebraicNumber (class in sage.rings.qqbar)
AlgebraicNumber_base (class in sage.rings.qqbar)
AlgebraicPolynomialTracker (class in sage.rings.qqbar)
AlgebraicReal (class in sage.rings.qqbar)
AlgebraicRealField (class in sage.rings.qqbar)
alpha() (sage.rings.number_field.number_field_element.CoordinateFunction method)
ambient() (sage.rings.number_field.order.Order method)
ambient_field (sage.rings.number_field.number_field_morphisms.EmbeddedNumberFieldConversion attribute)
(sage.rings.number_field.number_field_morphisms.EmbeddedNumberFieldMorphism attribute)
an_binop_element() (in module sage.rings.qqbar)
an_binop_expr() (in module sage.rings.qqbar)
an_binop_rational() (in module sage.rings.qqbar)
an_element() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
ANBinaryExpr (class in sage.rings.qqbar)
ANDescr (class in sage.rings.qqbar)
ANExtensionElement (class in sage.rings.qqbar)
angle() (sage.rings.qqbar.ANRational method)
ANRational (class in sage.rings.qqbar)
ANRoot (class in sage.rings.qqbar)
ANRootOfUnity (class in sage.rings.qqbar)
ANUnaryExpr (class in sage.rings.qqbar)
artin_symbol() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
as_hom() (sage.rings.number_field.galois_group.GaloisGroupElement method)
as_number_field_element() (sage.rings.qqbar.AlgebraicNumber_base method)
automorphisms() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)

B

bach_bound() (sage.rings.number_field.number_field_base.NumberField method)
base_field() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
base_ring() (sage.rings.number_field.number_field_rel.NumberField_relative method)
basis() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.AbsoluteOrder method)
(sage.rings.number_field.order.Order method)
(sage.rings.number_field.order.RelativeOrder method)
basis_to_module() (in module sage.rings.number_field.number_field_ideal)
bdd_height() (in module sage.rings.number_field.bdd_height)
bdd_height_iq() (in module sage.rings.number_field.bdd_height)
bdd_norm_pr_gens_iq() (in module sage.rings.number_field.bdd_height)
bdd_norm_pr_ideal_gens() (in module sage.rings.number_field.bdd_height)

C

cardinality() (sage.rings.number_field.morphism.NumberFieldHomset method)
ceil() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.AlgebraicReal method)
change_generator() (sage.rings.number_field.number_field.NumberField_generic method)
change_names() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.AbsoluteOrder method)
characteristic() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.qqbar.AlgebraicField_common method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
charpoly() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
(sage.rings.number_field.number_field_element.OrderElement_relative method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_element_quadratic.OrderElement_quadratic method)
class_group() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
class_number() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field.NumberField_quadratic method)
(sage.rings.number_field.order.Order method)
ClassGroup (class in sage.rings.number_field.class_group)
clear_denominators() (in module sage.rings.qqbar)
closest() (in module sage.rings.number_field.number_field_morphisms)
coefficients_to_power_sums() (in module sage.rings.number_field.totallyreal_phc)
common_polynomial() (sage.rings.qqbar.AlgebraicField_common method)
completion() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
complex_conjugation() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field.NumberField_generic method)
complex_embedding() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field_element.NumberFieldElement method)
complex_embeddings() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_element.NumberFieldElement method)
complex_exact() (sage.rings.qqbar.AlgebraicNumber method)
complex_number() (sage.rings.qqbar.AlgebraicNumber method)
complex_roots() (sage.rings.qqbar.AlgebraicPolynomialTracker method)
composite_fields() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
conductor() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
conjugate() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRoot method)
(sage.rings.qqbar.AlgebraicGenerator method)
(sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
conjugate_expand() (in module sage.rings.qqbar)
conjugate_shrink() (in module sage.rings.qqbar)
construction() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.qqbar.AlgebraicField method)
continued_fraction() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
continued_fraction_list() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
CoordinateFunction (class in sage.rings.number_field.number_field_element)
coordinates() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.Order method)
coordinates_in_terms_of_powers() (sage.rings.number_field.number_field_element.NumberFieldElement method)
create_embedding_from_approx() (in module sage.rings.number_field.number_field_morphisms)
create_key() (sage.rings.number_field.number_field.CyclotomicFieldFactory method)
create_key_and_extra_args() (sage.rings.number_field.number_field.NumberFieldFactory method)
create_object() (sage.rings.number_field.number_field.CyclotomicFieldFactory method)
(sage.rings.number_field.number_field.NumberFieldFactory method)
create_structure() (sage.rings.number_field.structure.AbsoluteFromRelative method)
(sage.rings.number_field.structure.NameChange method)
(sage.rings.number_field.structure.NumberFieldStructure method)
(sage.rings.number_field.structure.RelativeFromAbsolute method)
(sage.rings.number_field.structure.RelativeFromRelative method)
CyclotomicFieldEmbedding (class in sage.rings.number_field.number_field_morphisms)
CyclotomicFieldFactory (class in sage.rings.number_field.number_field)
CyclotomicFieldHomomorphism_im_gens (class in sage.rings.number_field.morphism)
CyclotomicFieldHomset (class in sage.rings.number_field.morphism)

D

decomposition_group() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
default_base_hom() (sage.rings.number_field.morphism.RelativeNumberFieldHomset method)
default_interval_prec() (sage.rings.qqbar.AlgebraicField_common method)
defining_polynomial() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
degree() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_base.NumberField method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.Order method)
(sage.rings.qqbar.AlgebraicNumber_base method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
denominator() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
denominator_ideal() (sage.rings.number_field.number_field_element.NumberFieldElement method)
descend_mod_power() (sage.rings.number_field.number_field_element.NumberFieldElement method)
different() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
disc() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
discriminant() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field.NumberField_quadratic method)
(sage.rings.number_field.number_field_base.NumberField method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.AbsoluteOrder method)
divides() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
do_polred() (in module sage.rings.qqbar)

E

E() (in module sage.rings.universal_cyclotomic_field)
each_is_integral() (in module sage.rings.number_field.order)
easy_is_irreducible_py() (in module sage.rings.number_field.totallyreal_data)
EisensteinIntegers() (in module sage.rings.number_field.order)
Element (sage.rings.number_field.class_group.ClassGroup attribute)
(sage.rings.number_field.class_group.SClassGroup attribute)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField attribute)
element_1_mod() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
elements_of_bounded_height() (sage.rings.number_field.number_field.NumberField_absolute method)
elements_of_norm() (sage.rings.number_field.number_field.NumberField_generic method)
EmbeddedNumberFieldConversion (class in sage.rings.number_field.number_field_morphisms)
EmbeddedNumberFieldMorphism (class in sage.rings.number_field.number_field_morphisms)
embeddings() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
enumerate_totallyreal_fields_all() (in module sage.rings.number_field.totallyreal_rel)
enumerate_totallyreal_fields_prim() (in module sage.rings.number_field.totallyreal)
enumerate_totallyreal_fields_rel() (in module sage.rings.number_field.totallyreal_rel)
EquationOrder() (in module sage.rings.number_field.order)
euler_phi() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
exactify() (sage.rings.qqbar.AlgebraicNumber_base method)
(sage.rings.qqbar.ANBinaryExpr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
(sage.rings.qqbar.ANRoot method)
(sage.rings.qqbar.ANUnaryExpr method)
(sage.rings.qqbar.AlgebraicPolynomialTracker method)
exp() (sage.rings.number_field.unit_group.UnitGroup method)
extension() (sage.rings.number_field.number_field.NumberField_generic method)

F

factor() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
factors() (sage.rings.qqbar.AlgebraicPolynomialTracker method)
field() (sage.rings.qqbar.AlgebraicGenerator method)
field_element_value() (sage.rings.qqbar.ANExtensionElement method)
field_order() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
find_zero_result() (in module sage.rings.qqbar)
fixed_field() (sage.rings.number_field.galois_group.GaloisGroup_subgroup method)
floor() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.AlgebraicReal method)
fraction_field() (sage.rings.number_field.order.Order method)
fractional_ideal() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
FractionalIdealClass (class in sage.rings.number_field.class_group)
free_module() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
(sage.rings.number_field.order.Order method)
fundamental_units() (sage.rings.number_field.unit_group.UnitGroup method)

G

galois_closure() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
galois_conjugate() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
galois_conjugates() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
galois_group() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
GaloisGroup (in module sage.rings.number_field.galois_group)
GaloisGroup_subgroup (class in sage.rings.number_field.galois_group)
GaloisGroup_v1 (class in sage.rings.number_field.galois_group)
GaloisGroup_v2 (class in sage.rings.number_field.galois_group)
GaloisGroupElement (class in sage.rings.number_field.galois_group)
GaussianIntegers() (in module sage.rings.number_field.order)
gcd() (sage.rings.number_field.number_field_element.NumberFieldElement method)
gen() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.Order method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
gen_embedding() (sage.rings.number_field.number_field.NumberField_generic method)
gen_image() (sage.rings.number_field.number_field_morphisms.NumberFieldEmbedding method)
generator() (sage.rings.qqbar.AlgebraicPolynomialTracker method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
gens() (sage.rings.number_field.class_group.FractionalIdealClass method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.Order method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
gens_ideals() (sage.rings.number_field.class_group.ClassGroup method)
gens_reduced() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
gens_two() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
get_AA_golden_ratio() (in module sage.rings.qqbar)
global_height() (sage.rings.number_field.number_field_element.NumberFieldElement method)
global_height_arch() (sage.rings.number_field.number_field_element.NumberFieldElement method)
global_height_non_arch() (sage.rings.number_field.number_field_element.NumberFieldElement method)
group() (sage.rings.number_field.galois_group.GaloisGroup_v1 method)

H

handle_sage_input() (sage.rings.qqbar.ANBinaryExpr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
(sage.rings.qqbar.ANRoot method)
(sage.rings.qqbar.ANUnaryExpr method)
hermite_constant() (in module sage.rings.number_field.totallyreal_data)
hilbert_class_field() (sage.rings.number_field.number_field.NumberField_quadratic method)
hilbert_class_field_defining_polynomial() (sage.rings.number_field.number_field.NumberField_quadratic method)
hilbert_class_polynomial() (sage.rings.number_field.number_field.NumberField_quadratic method)
hilbert_conductor() (sage.rings.number_field.number_field.NumberField_absolute method)
hilbert_symbol() (sage.rings.number_field.number_field.NumberField_absolute method)

I

ideal() (sage.rings.number_field.class_group.FractionalIdealClass method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
ideal_below() (sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
ideal_class_log() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
idealcoprime() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
ideallog() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
ideals_of_bdd_norm() (sage.rings.number_field.number_field.NumberField_generic method)
idealstar() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
im_gens() (sage.rings.number_field.morphism.RelativeNumberFieldHomomorphism_from_abs method)
imag() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
imag_part() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
incr() (sage.rings.number_field.totallyreal_rel.tr_data_rel method)
increment() (sage.rings.number_field.totallyreal_data.tr_data method)
index_in() (sage.rings.number_field.order.AbsoluteOrder method)
(sage.rings.number_field.order.RelativeOrder method)
inertia_group() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
int_has_small_square_divisor() (in module sage.rings.number_field.totallyreal_data)
integer_points_in_polytope() (in module sage.rings.number_field.bdd_height)
integral_basis() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
integral_closure() (sage.rings.number_field.order.Order method)
integral_elements_in_box() (in module sage.rings.number_field.totallyreal_rel)
integral_split() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
intersection() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.AbsoluteOrder method)
interval() (sage.rings.qqbar.AlgebraicNumber_base method)
interval_diameter() (sage.rings.qqbar.AlgebraicNumber_base method)
interval_exact() (sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
interval_fast() (sage.rings.qqbar.AlgebraicNumber_base method)
inverse() (sage.rings.number_field.class_group.FractionalIdealClass method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
inverse_mod() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element.OrderElement_absolute method)
(sage.rings.number_field.number_field_element.OrderElement_relative method)
(sage.rings.number_field.number_field_element_quadratic.OrderElement_quadratic method)
invert() (sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
invertible_residues() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
invertible_residues_mod() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
is_absolute() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_base.NumberField method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
is_AbsoluteNumberField() (in module sage.rings.number_field.number_field)
is_AlgebraicField() (in module sage.rings.qqbar)
is_AlgebraicField_common() (in module sage.rings.qqbar)
is_AlgebraicNumber() (in module sage.rings.qqbar)
is_AlgebraicReal() (in module sage.rings.qqbar)
is_AlgebraicRealField() (in module sage.rings.qqbar)
is_CM() (sage.rings.number_field.number_field.NumberField_generic method)
is_CM_extension() (sage.rings.number_field.number_field_rel.NumberField_relative method)
is_complex() (sage.rings.qqbar.AlgebraicGenerator method)
(sage.rings.qqbar.ANBinaryExpr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
(sage.rings.qqbar.ANRoot method)
(sage.rings.qqbar.ANUnaryExpr method)
(sage.rings.qqbar.AlgebraicPolynomialTracker method)
is_coprime() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
is_CyclotomicField() (in module sage.rings.number_field.number_field)
is_exact() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
is_field() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
is_finite() (sage.rings.number_field.number_field_base.NumberField method)
(sage.rings.qqbar.AlgebraicField_common method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
is_free() (sage.rings.number_field.number_field_rel.NumberField_relative method)
is_fundamental_discriminant() (in module sage.rings.number_field.number_field)
is_galois() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field.NumberField_quadratic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
is_galois_absolute() (sage.rings.number_field.number_field_rel.NumberField_relative method)
is_galois_relative() (sage.rings.number_field.number_field_rel.NumberField_relative method)
is_injective() (sage.rings.number_field.maps.NumberFieldIsomorphism method)
is_integer() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.AlgebraicNumber_base method)
is_integral() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
is_integrally_closed() (sage.rings.number_field.order.Order method)
is_isomorphic() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
is_isomorphic_relative() (sage.rings.number_field.number_field_rel.NumberField_relative method)
is_maximal() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.Order method)
is_noetherian() (sage.rings.number_field.order.Order method)
is_norm() (sage.rings.number_field.number_field_element.NumberFieldElement method)
is_nth_power() (sage.rings.number_field.number_field_element.NumberFieldElement method)
is_NumberField() (in module sage.rings.number_field.number_field_base)
is_NumberFieldElement() (in module sage.rings.number_field.number_field_element)
is_NumberFieldFractionalIdeal() (in module sage.rings.number_field.number_field_ideal)
is_NumberFieldFractionalIdeal_rel() (in module sage.rings.number_field.number_field_ideal_rel)
is_NumberFieldHomsetCodomain() (in module sage.rings.number_field.number_field)
is_NumberFieldIdeal() (in module sage.rings.number_field.number_field_ideal)
is_NumberFieldOrder() (in module sage.rings.number_field.order)
is_one() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
is_prime() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
is_principal() (sage.rings.number_field.class_group.FractionalIdealClass method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
is_QuadraticField() (in module sage.rings.number_field.number_field)
is_rational() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
is_real() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
is_real_positive() (sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
is_relative() (sage.rings.number_field.number_field.NumberField_generic method)
is_RelativeNumberField() (in module sage.rings.number_field.number_field_rel)
is_S_integral() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
is_S_unit() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
is_simple() (sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
is_square() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.AlgebraicNumber_base method)
is_suborder() (sage.rings.number_field.order.Order method)
(sage.rings.number_field.order.RelativeOrder method)
is_surjective() (sage.rings.number_field.maps.NumberFieldIsomorphism method)
is_totally_imaginary() (sage.rings.number_field.number_field.NumberField_generic method)
is_totally_positive() (sage.rings.number_field.number_field_element.NumberFieldElement method)
is_totally_real() (sage.rings.number_field.number_field.NumberField_generic method)
is_trivial() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.qqbar.AlgebraicGenerator method)
is_unit() (sage.rings.number_field.number_field_element.NumberFieldElement method)
is_zero() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
isolating_interval() (in module sage.rings.qqbar)

K

key() (sage.rings.number_field.splitting_field.SplittingData method)
krull_dimension() (sage.rings.number_field.order.Order method)

L

lagrange_degree_3() (in module sage.rings.number_field.totallyreal_data)
late_import() (in module sage.rings.universal_cyclotomic_field)
latex_variable_name() (sage.rings.number_field.number_field.NumberField_generic method)
lift() (sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
lift_to_base() (sage.rings.number_field.number_field_rel.NumberField_relative method)
LiftMap (class in sage.rings.number_field.number_field_ideal)
list() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.morphism.CyclotomicFieldHomset method)
(sage.rings.number_field.morphism.NumberFieldHomset method)
(sage.rings.number_field.morphism.RelativeNumberFieldHomset method)
(sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
local_height() (sage.rings.number_field.number_field_element.NumberFieldElement method)
local_height_arch() (sage.rings.number_field.number_field_element.NumberFieldElement method)
log() (sage.rings.number_field.unit_group.UnitGroup method)

M

MapAbsoluteToRelativeNumberField (class in sage.rings.number_field.maps)
MapNumberFieldToVectorSpace (class in sage.rings.number_field.maps)
MapRelativeNumberFieldToRelativeVectorSpace (class in sage.rings.number_field.maps)
MapRelativeNumberFieldToVectorSpace (class in sage.rings.number_field.maps)
MapRelativeToAbsoluteNumberField (class in sage.rings.number_field.maps)
MapRelativeVectorSpaceToRelativeNumberField (class in sage.rings.number_field.maps)
MapVectorSpaceToNumberField (class in sage.rings.number_field.maps)
MapVectorSpaceToRelativeNumberField (class in sage.rings.number_field.maps)
matching_root() (in module sage.rings.number_field.number_field_morphisms)
matrix() (sage.rings.number_field.number_field_element.NumberFieldElement method)
maximal_order() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_base.NumberField method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
maximal_totally_real_subfield() (sage.rings.number_field.number_field.NumberField_generic method)
minkowski_bound() (sage.rings.number_field.number_field_base.NumberField method)
Minkowski_embedding() (sage.rings.number_field.number_field.NumberField_absolute method)
minpoly() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element.NumberFieldElement_absolute method)
(sage.rings.number_field.number_field_element.OrderElement_relative method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_element_quadratic.OrderElement_quadratic method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
(sage.rings.qqbar.AlgebraicNumber_base method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
module() (sage.rings.number_field.order.AbsoluteOrder method)
multiplicative_order() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)

N

NameChange (class in sage.rings.number_field.structure)
NameChangeMap (class in sage.rings.number_field.maps)
narrow_class_group() (sage.rings.number_field.number_field.NumberField_generic method)
neg() (sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
next() (sage.rings.number_field.small_primes_of_degree_one.Small_primes_of_degree_one_iter method)
next_split_prime() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
ngens() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.order.Order method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
norm() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_element_quadratic.OrderElement_quadratic method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.AlgebraicNumber method)
norm_of_galois_extension() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
nth_root() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.AlgebraicNumber_base method)
number_field() (sage.rings.number_field.class_group.ClassGroup method)
(sage.rings.number_field.galois_group.GaloisGroup_v1 method)
(sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.Order method)
(sage.rings.number_field.unit_group.UnitGroup method)
number_field_elements_from_algebraics() (in module sage.rings.qqbar)
number_of_roots_of_unity() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
NumberField (class in sage.rings.number_field.number_field_base)
NumberField() (in module sage.rings.number_field.number_field)
NumberField_absolute (class in sage.rings.number_field.number_field)
NumberField_absolute_v1() (in module sage.rings.number_field.number_field)
NumberField_cyclotomic (class in sage.rings.number_field.number_field)
NumberField_cyclotomic_v1() (in module sage.rings.number_field.number_field)
NumberField_extension_v1() (in module sage.rings.number_field.number_field_rel)
NumberField_generic (class in sage.rings.number_field.number_field)
NumberField_generic_v1() (in module sage.rings.number_field.number_field)
NumberField_quadratic (class in sage.rings.number_field.number_field)
NumberField_quadratic_v1() (in module sage.rings.number_field.number_field)
NumberField_relative (class in sage.rings.number_field.number_field_rel)
NumberField_relative_v1() (in module sage.rings.number_field.number_field_rel)
NumberFieldElement (class in sage.rings.number_field.number_field_element)
NumberFieldElement_absolute (class in sage.rings.number_field.number_field_element)
NumberFieldElement_quadratic (class in sage.rings.number_field.number_field_element_quadratic)
NumberFieldElement_relative (class in sage.rings.number_field.number_field_element)
NumberFieldEmbedding (class in sage.rings.number_field.number_field_morphisms)
NumberFieldFactory (class in sage.rings.number_field.number_field)
NumberFieldFractionalIdeal (class in sage.rings.number_field.number_field_ideal)
NumberFieldFractionalIdeal_rel (class in sage.rings.number_field.number_field_ideal_rel)
NumberFieldHomomorphism_im_gens (class in sage.rings.number_field.morphism)
NumberFieldHomset (class in sage.rings.number_field.morphism)
NumberFieldIdeal (class in sage.rings.number_field.number_field_ideal)
NumberFieldIsomorphism (class in sage.rings.number_field.maps)
NumberFieldStructure (class in sage.rings.number_field.structure)
NumberFieldTower() (in module sage.rings.number_field.number_field)
numerator() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
numerator_ideal() (sage.rings.number_field.number_field_element.NumberFieldElement method)

O

odlyzko_bound_totallyreal() (in module sage.rings.number_field.totallyreal)
OK() (sage.rings.number_field.number_field_base.NumberField method)
one() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
optimized_representation() (sage.rings.number_field.number_field.NumberField_absolute method)
optimized_subfields() (sage.rings.number_field.number_field.NumberField_absolute method)
ord() (sage.rings.number_field.number_field_element.NumberFieldElement method)
Order (class in sage.rings.number_field.order)
order() (sage.rings.number_field.galois_group.GaloisGroup_v1 method)
(sage.rings.number_field.morphism.NumberFieldHomset method)
(sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.qqbar.AlgebraicField_common method)
OrderElement_absolute (class in sage.rings.number_field.number_field_element)
OrderElement_quadratic (class in sage.rings.number_field.number_field_element_quadratic)
OrderElement_relative (class in sage.rings.number_field.number_field_element)

P

pari_absolute_base_polynomial() (sage.rings.number_field.number_field_rel.NumberField_relative method)
pari_bnf() (sage.rings.number_field.number_field.NumberField_generic method)
pari_field() (sage.rings.qqbar.AlgebraicGenerator method)
pari_hnf() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
pari_nf() (sage.rings.number_field.number_field.NumberField_generic method)
pari_polynomial() (sage.rings.number_field.number_field.NumberField_generic method)
pari_prime() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
pari_relative_polynomial() (sage.rings.number_field.number_field_rel.NumberField_relative method)
pari_rhnf() (sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
pari_rnf() (sage.rings.number_field.number_field_rel.NumberField_relative method)
pari_rnfnorm_data() (sage.rings.number_field.number_field.NumberField_generic method)
pari_zk() (sage.rings.number_field.number_field.NumberField_generic method)
parts() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
places() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
poldegree() (sage.rings.number_field.splitting_field.SplittingData method)
poly() (sage.rings.qqbar.AlgebraicPolynomialTracker method)
polynomial() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
polynomial_ntl() (sage.rings.number_field.number_field.NumberField_generic method)
polynomial_quotient_ring() (sage.rings.number_field.number_field.NumberField_generic method)
polynomial_ring() (sage.rings.number_field.number_field.NumberField_generic method)
polynomial_root() (sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
power_basis() (sage.rings.number_field.number_field.NumberField_generic method)
prec_seq() (in module sage.rings.qqbar)
preimage() (sage.rings.number_field.morphism.NumberFieldHomomorphism_im_gens method)
prime_above() (sage.rings.number_field.number_field.NumberField_generic method)
prime_factors() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
prime_to_idealM_part() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
prime_to_S_part() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
primes() (sage.rings.number_field.unit_group.UnitGroup method)
primes_above() (sage.rings.number_field.number_field.NumberField_generic method)
primes_of_bounded_norm() (sage.rings.number_field.number_field.NumberField_generic method)
primes_of_bounded_norm_iter() (sage.rings.number_field.number_field.NumberField_generic method)
primes_of_degree_one_iter() (sage.rings.number_field.number_field.NumberField_generic method)
primes_of_degree_one_list() (sage.rings.number_field.number_field.NumberField_generic method)
primitive_element() (sage.rings.number_field.number_field.NumberField_generic method)
primitive_root_of_unity() (sage.rings.number_field.number_field.NumberField_generic method)
printa() (sage.rings.number_field.totallyreal_data.tr_data method)
proof_flag() (in module sage.rings.number_field.number_field)
put_natural_embedding_first() (in module sage.rings.number_field.number_field)

Q

Q_to_quadratic_field_element (class in sage.rings.number_field.number_field_element_quadratic)
QuadraticField() (in module sage.rings.number_field.number_field)
quotient_char_p() (in module sage.rings.number_field.number_field_ideal)
QuotientMap (class in sage.rings.number_field.number_field_ideal)

R

radical_expression() (sage.rings.qqbar.AlgebraicNumber_base method)
ramification_breaks() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
ramification_degree() (sage.rings.number_field.galois_group.GaloisGroupElement method)
ramification_group() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
ramification_index() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
random_element() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.order.Order method)
(sage.rings.qqbar.AlgebraicField method)
rank() (sage.rings.number_field.order.Order method)
(sage.rings.number_field.unit_group.UnitGroup method)
rational_argument() (sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
rational_exact_root() (in module sage.rings.qqbar)
ray_class_number() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
real() (sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
real_embeddings() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
real_exact() (sage.rings.qqbar.AlgebraicReal method)
real_number() (sage.rings.qqbar.AlgebraicReal method)
real_part() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
real_places() (sage.rings.number_field.number_field.NumberField_absolute method)
reduce() (sage.rings.number_field.class_group.FractionalIdealClass method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
reduce_equiv() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
reduced_basis() (sage.rings.number_field.number_field.NumberField_generic method)
reduced_gram_matrix() (sage.rings.number_field.number_field.NumberField_generic method)
refine_embedding() (in module sage.rings.number_field.number_field)
refine_interval() (sage.rings.qqbar.ANRoot method)
regulator() (sage.rings.number_field.number_field.NumberField_generic method)
relative_degree() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
relative_different() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
relative_discriminant() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
relative_norm() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
relative_order_from_ring_generators() (in module sage.rings.number_field.order)
relative_polynomial() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
relative_ramification_index() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
relative_vector_space() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
RelativeFromAbsolute (class in sage.rings.number_field.structure)
RelativeFromRelative (class in sage.rings.number_field.structure)
RelativeNumberFieldHomomorphism_from_abs (class in sage.rings.number_field.morphism)
RelativeNumberFieldHomset (class in sage.rings.number_field.morphism)
RelativeOrder (class in sage.rings.number_field.order)
relativize() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
representative_prime() (sage.rings.number_field.class_group.FractionalIdealClass method)
residue_class_degree() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
residue_field() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.order.Order method)
residue_symbol() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
residues() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
ring_generators() (sage.rings.number_field.order.Order method)
ring_of_integers() (sage.rings.number_field.number_field_base.NumberField method)
root_as_algebraic() (sage.rings.qqbar.AlgebraicGenerator method)
root_from_approx() (in module sage.rings.number_field.number_field_morphisms)
roots_of_unity() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
(sage.rings.number_field.unit_group.UnitGroup method)
round() (sage.rings.qqbar.AlgebraicReal method)

S

S() (sage.rings.number_field.class_group.SClassGroup method)
S_class_group() (sage.rings.number_field.number_field.NumberField_generic method)
S_ideal_class_log() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
S_unit_group() (sage.rings.number_field.number_field.NumberField_generic method)
S_units() (sage.rings.number_field.number_field.NumberField_generic method)
sage.rings.number_field.bdd_height (module)
sage.rings.number_field.class_group (module)
sage.rings.number_field.galois_group (module)
sage.rings.number_field.maps (module)
sage.rings.number_field.morphism (module)
sage.rings.number_field.number_field (module)
sage.rings.number_field.number_field_base (module)
sage.rings.number_field.number_field_element (module)
sage.rings.number_field.number_field_element_quadratic (module)
sage.rings.number_field.number_field_ideal (module)
sage.rings.number_field.number_field_ideal_rel (module)
sage.rings.number_field.number_field_morphisms (module)
sage.rings.number_field.number_field_rel (module)
sage.rings.number_field.order (module)
sage.rings.number_field.small_primes_of_degree_one (module)
sage.rings.number_field.splitting_field (module)
sage.rings.number_field.structure (module)
sage.rings.number_field.totallyreal (module)
sage.rings.number_field.totallyreal_data (module)
sage.rings.number_field.totallyreal_phc (module)
sage.rings.number_field.totallyreal_rel (module)
sage.rings.number_field.unit_group (module)
sage.rings.qqbar (module)
sage.rings.universal_cyclotomic_field (module)
scale() (sage.rings.qqbar.ANRational method)
SClassGroup (class in sage.rings.number_field.class_group)
section() (sage.rings.number_field.number_field_morphisms.EmbeddedNumberFieldMorphism method)
selmer_group() (sage.rings.number_field.number_field.NumberField_generic method)
selmer_group_iterator() (sage.rings.number_field.number_field.NumberField_generic method)
SFractionalIdealClass (class in sage.rings.number_field.class_group)
short_prec_seq() (in module sage.rings.qqbar)
sign() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.qqbar.AlgebraicReal method)
signature() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_base.NumberField method)
simplify() (sage.rings.qqbar.AlgebraicNumber_base method)
(sage.rings.qqbar.ANExtensionElement method)
Small_primes_of_degree_one_iter (class in sage.rings.number_field.small_primes_of_degree_one)
small_residue() (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal method)
smallest_integer() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
solve_CRT() (sage.rings.number_field.number_field.NumberField_generic method)
some_elements() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
specified_complex_embedding() (sage.rings.number_field.number_field.NumberField_generic method)
splitting_field() (in module sage.rings.number_field.splitting_field)
(sage.rings.number_field.galois_group.GaloisGroup_v2 method)
SplittingData (class in sage.rings.number_field.splitting_field)
SplittingFieldAbort
sqrt() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.AlgebraicNumber_base method)
structure() (sage.rings.number_field.number_field.NumberField_generic method)
subfield() (sage.rings.number_field.number_field.NumberField_generic method)
subfields() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
subgroup() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
super_poly() (sage.rings.qqbar.AlgebraicGenerator method)
support() (sage.rings.number_field.number_field_element.NumberFieldElement method)

T

t1 (in module sage.rings.qqbar)
t2 (in module sage.rings.qqbar)
tail_prec_seq() (in module sage.rings.qqbar)
timestr() (in module sage.rings.number_field.totallyreal)
to_cyclotomic_field() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
torsion_generator() (sage.rings.number_field.unit_group.UnitGroup method)
tr_data (class in sage.rings.number_field.totallyreal_data)
tr_data_rel (class in sage.rings.number_field.totallyreal_rel)
trace() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(sage.rings.number_field.number_field_element_quadratic.OrderElement_quadratic method)
trace_dual_basis() (sage.rings.number_field.number_field.NumberField_generic method)
trace_pairing() (sage.rings.number_field.number_field.NumberField_generic method)
trunc() (sage.rings.qqbar.AlgebraicReal method)

U

UCFtoQQbar (class in sage.rings.universal_cyclotomic_field)
uniformizer() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)
union() (sage.rings.qqbar.AlgebraicGenerator method)
unit_group() (sage.rings.number_field.number_field.NumberField_generic method)
UnitGroup (class in sage.rings.number_field.unit_group)
units() (sage.rings.number_field.number_field.NumberField_generic method)
UniversalCyclotomicField (class in sage.rings.universal_cyclotomic_field)
UniversalCyclotomicFieldElement (class in sage.rings.universal_cyclotomic_field)

V

valuation() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element.NumberFieldElement_relative method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
vector() (sage.rings.number_field.number_field_element.NumberFieldElement method)
vector_space() (sage.rings.number_field.number_field.NumberField_absolute method)
(sage.rings.number_field.number_field_rel.NumberField_relative method)

W

weed_fields() (in module sage.rings.number_field.totallyreal)

Z

Z_to_quadratic_field_element (class in sage.rings.number_field.number_field_element_quadratic)
zero() (sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
zeta() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
(sage.rings.number_field.unit_group.UnitGroup method)
(sage.rings.qqbar.AlgebraicField method)
(sage.rings.qqbar.AlgebraicRealField method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
zeta_coefficients() (sage.rings.number_field.number_field.NumberField_generic method)
zeta_function() (sage.rings.number_field.number_field.NumberField_generic method)
zeta_order() (sage.rings.number_field.number_field.NumberField_cyclotomic method)
(sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.unit_group.UnitGroup method)