Navigation
index
modules
|
Sage 9.2 Reference Manual: Algebraic Numbers and Number Fields
»
Index
Index
_
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
K
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
U
|
V
|
W
|
Y
|
Z
_
_richcmp_() (sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
A
AA (in module sage.rings.qqbar)
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)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
abs_hom() (sage.rings.number_field.morphism.RelativeNumberFieldHomomorphism_from_abs method)
abs_non_arch() (sage.rings.number_field.number_field_element.NumberFieldElement method)
abs_val() (sage.rings.number_field.number_field.NumberField_absolute 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_element.NumberFieldElement 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)
AlgebraicField_common.options() (in module 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)
AlgebraicNumberPowQQAction (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)
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)
beta_k() (in module sage.rings.number_field.S_unit_solver)
C
c11_func() (in module sage.rings.number_field.S_unit_solver)
c13_func() (in module sage.rings.number_field.S_unit_solver)
c3_func() (in module sage.rings.number_field.S_unit_solver)
c4_func() (in module sage.rings.number_field.S_unit_solver)
cardinality() (sage.rings.number_field.homset.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)
clean_rfv_dict() (in module sage.rings.number_field.S_unit_solver)
clean_sfs() (in module sage.rings.number_field.S_unit_solver)
clear_denominators() (in module sage.rings.qqbar)
closest() (in module sage.rings.number_field.number_field_morphisms)
cmp_elements_with_same_minpoly() (in module sage.rings.qqbar)
coefficients_to_power_sums() (in module sage.rings.number_field.totallyreal_phc)
column_Log() (in module sage.rings.number_field.S_unit_solver)
common_polynomial() (sage.rings.qqbar.AlgebraicField_common method)
compatible_system_lift() (in module sage.rings.number_field.S_unit_solver)
compatible_systems() (in module sage.rings.number_field.S_unit_solver)
compatible_vectors() (in module sage.rings.number_field.S_unit_solver)
compatible_vectors_check() (in module sage.rings.number_field.S_unit_solver)
completely_split_primes() (sage.rings.number_field.number_field.NumberField_generic 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.number_field.number_field.NumberField_generic method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
conjugate() (sage.rings.number_field.number_field_element.NumberFieldElement method)
(sage.rings.qqbar.AlgebraicGenerator method)
(sage.rings.qqbar.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRoot method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
conjugate_expand() (in module sage.rings.qqbar)
conjugate_shrink() (in module sage.rings.qqbar)
construct_comp_exp_vec() (in module sage.rings.number_field.S_unit_solver)
construct_complement_dictionaries() (in module sage.rings.number_field.S_unit_solver)
construct_rfv_to_ev() (in module sage.rings.number_field.S_unit_solver)
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)
cx_LLL_bound() (in module sage.rings.number_field.S_unit_solver)
CyclotomicFieldConversion (class in sage.rings.number_field.number_field_morphisms)
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.homset)
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.homset.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)
defining_polynomial_for_Kp() (in module sage.rings.number_field.S_unit_solver)
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_element.NumberFieldElement 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)
drop_vector() (in module sage.rings.number_field.S_unit_solver)
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.number_field.galois_group.GaloisGroup_v2 attribute)
(sage.rings.number_field.homset.CyclotomicFieldHomset attribute)
(sage.rings.number_field.homset.NumberFieldHomset attribute)
(sage.rings.number_field.homset.RelativeNumberFieldHomset 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)
embedding_to_Kp() (in module sage.rings.number_field.S_unit_solver)
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)
eq_up_to_order() (in module sage.rings.number_field.S_unit_solver)
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.AlgebraicPolynomialTracker 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)
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)
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.NumberField_absolute method)
(sage.rings.number_field.number_field_ideal.NumberFieldIdeal method)
(sage.rings.number_field.number_field_ideal_rel.NumberFieldFractionalIdeal_rel method)
(sage.rings.number_field.number_field_rel.NumberField_relative 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.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)
hilbert_symbol_negative_at_S() (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.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.qqbar.ANDescr 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_abelian() (sage.rings.number_field.number_field.NumberField_generic 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.AlgebraicPolynomialTracker 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)
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_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)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement 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_padic_square() (sage.rings.number_field.number_field_element.NumberFieldElement 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_place() (in module sage.rings.number_field.number_field)
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)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement 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
K0_func() (in module sage.rings.number_field.S_unit_solver)
K1_func() (in module sage.rings.number_field.S_unit_solver)
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.homset.CyclotomicFieldHomset method)
(sage.rings.number_field.homset.NumberFieldHomset method)
(sage.rings.number_field.homset.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)
lmfdb_page() (sage.rings.number_field.number_field.NumberField_generic 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)
log_p() (in module sage.rings.number_field.S_unit_solver)
log_p_series_part() (in module sage.rings.number_field.S_unit_solver)
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)
minimal_vector() (in module sage.rings.number_field.S_unit_solver)
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.AlgebraicNumber_base method)
(sage.rings.qqbar.ANExtensionElement method)
(sage.rings.qqbar.ANRational method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
module
sage.rings.number_field.bdd_height
sage.rings.number_field.class_group
sage.rings.number_field.galois_group
sage.rings.number_field.homset
sage.rings.number_field.maps
sage.rings.number_field.morphism
sage.rings.number_field.number_field
sage.rings.number_field.number_field_base
sage.rings.number_field.number_field_element
sage.rings.number_field.number_field_element_quadratic
sage.rings.number_field.number_field_ideal
sage.rings.number_field.number_field_ideal_rel
sage.rings.number_field.number_field_morphisms
sage.rings.number_field.number_field_rel
sage.rings.number_field.order
sage.rings.number_field.S_unit_solver
sage.rings.number_field.small_primes_of_degree_one
sage.rings.number_field.splitting_field
sage.rings.number_field.structure
sage.rings.number_field.totallyreal
sage.rings.number_field.totallyreal_data
sage.rings.number_field.totallyreal_phc
sage.rings.number_field.totallyreal_rel
sage.rings.number_field.unit_group
sage.rings.qqbar
sage.rings.universal_cyclotomic_field
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.qqbar.AlgebraicReal method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
mus() (in module sage.rings.number_field.S_unit_solver)
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.AlgebraicNumber method)
(sage.rings.qqbar.ANDescr method)
(sage.rings.qqbar.ANExtensionElement 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.NumberField_quadratic 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.homset)
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)
Omega_prime() (in module sage.rings.number_field.S_unit_solver)
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.homset.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
p_adic_LLL_bound() (in module sage.rings.number_field.S_unit_solver)
p_adic_LLL_bound_one_prime() (in module sage.rings.number_field.S_unit_solver)
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)
possible_mu0s() (in module sage.rings.number_field.S_unit_solver)
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)
QQbar (in module sage.rings.qqbar)
quadratic_defect() (sage.rings.number_field.number_field.NumberField_generic method)
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.AlgebraicNumber method)
(sage.rings.qqbar.AlgebraicReal method)
(sage.rings.qqbar.ANDescr 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)
reduction_step_complex_case() (in module sage.rings.number_field.S_unit_solver)
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.homset)
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.number_field.number_field_element.NumberFieldElement method)
(sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic method)
(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_unit_solutions() (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.homset
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.S_unit_solver
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.CyclotomicFieldEmbedding method)
(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)
sieve_below_bound() (in module sage.rings.number_field.S_unit_solver)
sieve_ordering() (in module sage.rings.number_field.S_unit_solver)
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)
solutions_from_systems() (in module sage.rings.number_field.S_unit_solver)
solve_CRT() (sage.rings.number_field.number_field.NumberField_generic method)
solve_S_unit_equation() (in module sage.rings.number_field.S_unit_solver)
some_elements() (sage.rings.number_field.number_field.NumberField_generic method)
(sage.rings.number_field.order.Order method)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicField method)
specified_complex_embedding() (sage.rings.number_field.number_field.NumberField_generic method)
split_primes_large_lcm() (in module sage.rings.number_field.S_unit_solver)
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)
(sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method)
structure() (sage.rings.number_field.number_field.NumberField_generic method)
subfield() (sage.rings.number_field.number_field.NumberField_generic method)
subfield_from_elements() (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)
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
UCF_sqrt_int() (in module sage.rings.universal_cyclotomic_field)
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)
unrank() (sage.rings.number_field.galois_group.GaloisGroup_v2 method)
V
valuation() (sage.rings.number_field.number_field.NumberField_generic method)
(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)
(sage.rings.number_field.order.Order method)
vector() (sage.rings.number_field.number_field_element.NumberFieldElement method)
vector_space() (sage.rings.number_field.number_field_rel.NumberField_relative method)
W
weed_fields() (in module sage.rings.number_field.totallyreal)
Y
Yu_a1_kappa1_c1() (in module sage.rings.number_field.S_unit_solver)
Yu_bound() (in module sage.rings.number_field.S_unit_solver)
Yu_C1_star() (in module sage.rings.number_field.S_unit_solver)
Yu_condition_115() (in module sage.rings.number_field.S_unit_solver)
Yu_modified_height() (in module sage.rings.number_field.S_unit_solver)
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)
Quick search
Navigation
index
modules
|
Sage 9.2 Reference Manual: Algebraic Numbers and Number Fields
»
Index