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 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.Order_absolute method) (sage.rings.number_field.order.Order_relative 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.Order_absolute method) (sage.rings.number_field.order.Order_relative 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) AbsoluteOrderFactory (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) 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.Order method) (sage.rings.number_field.order.Order_absolute method) (sage.rings.number_field.order.Order_relative method) basis_for_p_cokernel() (in module sage.rings.number_field.selmer_group) 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.Order_absolute 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.number_field.order.Order method) (sage.rings.universal_cyclotomic_field.UniversalCyclotomicFieldElement method) conjugate() (sage.rings.number_field.number_field_element.NumberFieldElement method) (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic 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) coords_in_U_mod_p() (in module sage.rings.number_field.selmer_group) 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) (sage.rings.number_field.order.AbsoluteOrderFactory method) (sage.rings.number_field.order.RelativeOrderFactory method) create_object() (sage.rings.number_field.number_field.CyclotomicFieldFactory method) (sage.rings.number_field.number_field.NumberFieldFactory method) (sage.rings.number_field.order.AbsoluteOrderFactory method) (sage.rings.number_field.order.RelativeOrderFactory 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) decomposition_type() (sage.rings.number_field.number_field.NumberField_generic 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_element_quadratic.NumberFieldElement_quadratic_sqrt method) (sage.rings.number_field.number_field_element_quadratic.OrderElement_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) dirichlet_group() (sage.rings.number_field.number_field.NumberField_generic 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.Order_absolute 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) easy_order() (sage.rings.number_field.galois_group.GaloisGroup_v2 method) 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_subgroup 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.NumberField_cyclotomic 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) (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_generic 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) 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) GaussianField() (in module sage.rings.number_field.number_field) 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) (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic method) gens_two() (sage.rings.number_field.number_field_ideal.NumberFieldIdeal method) (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic method) get_AA_golden_ratio() (in module sage.rings.qqbar) get_object() (sage.rings.number_field.order.OrderFactory method) 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) (sage.rings.number_field.galois_group.GaloisGroup_v2 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) idealchinese() (sage.rings.number_field.number_field.NumberField_generic 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_gaussian method) (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.number_field.number_field_element_quadratic.NumberFieldElement_gaussian method) (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.Order_absolute method) (sage.rings.number_field.order.Order_relative 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.Order_absolute 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_cyclotomic method) (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_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_equivalent() (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic method) 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.qqbar.AlgebraicNumber_base 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_absolute method) (sage.rings.number_field.order.Order_relative 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_element.NumberFieldElement method) (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) (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic method) 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_sqrt_disc() (in module sage.rings.number_field.number_field_element_quadratic) 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.Order_relative 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) 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.number_field_element_quadratic.NumberFieldElement_gaussian method) (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) logarithmic_embedding() (sage.rings.number_field.number_field.NumberField_absolute method) (sage.rings.number_field.number_field_rel.NumberField_relative 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_generic method) (sage.rings.number_field.number_field_base.NumberField 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.order_ideal sage.rings.number_field.S_unit_solver sage.rings.number_field.selmer_group 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.Order_absolute 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.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.number_field.order_ideal.NumberFieldOrderIdeal_generic 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_gaussian (class in sage.rings.number_field.number_field_element_quadratic) NumberFieldElement_quadratic (class in sage.rings.number_field.number_field_element_quadratic) NumberFieldElement_quadratic_sqrt (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) NumberFieldOrderIdeal() (in module sage.rings.number_field.order_ideal) NumberFieldOrderIdeal_generic (class in sage.rings.number_field.order_ideal) NumberFieldOrderIdeal_quadratic (class in sage.rings.number_field.order_ideal) 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) options (sage.rings.qqbar.AlgebraicField_common attribute) 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.galois_group.GaloisGroup_v2 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) Order_absolute (class in sage.rings.number_field.order) order_of_conductor() (sage.rings.number_field.number_field.NumberField_quadratic method) Order_relative (class in sage.rings.number_field.order) 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) OrderFactory (class in sage.rings.number_field.order) 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_label() (sage.rings.number_field.galois_group.GaloisGroup_v2 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) pSelmerGroup() (in module sage.rings.number_field.selmer_group) 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) quadratic_defect() (sage.rings.number_field.number_field.NumberField_generic method) quadratic_form() (sage.rings.number_field.order_ideal.NumberFieldOrderIdeal_quadratic method) quadratic_order_class_number() (in module sage.rings.number_field.order) 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) (sage.rings.qqbar.AlgebraicRealField 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_gaussian method) (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.number_field.number_field_element_quadratic.NumberFieldElement_gaussian method) (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_data() (sage.rings.number_field.order.AbsoluteOrderFactory 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) RelativeOrderFactory (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.order_ideal module sage.rings.number_field.S_unit_solver module sage.rings.number_field.selmer_group 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_generators() (sage.rings.number_field.number_field.NumberField_generic method) selmer_group_iterator() (sage.rings.number_field.number_field.NumberField_generic method) selmer_space() (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.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_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) 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 attribute) super_poly() (sage.rings.qqbar.AlgebraicGenerator method) support() (sage.rings.number_field.number_field_element.NumberFieldElement method) (sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal 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) transitive_number() (sage.rings.number_field.galois_group.GaloisGroup_v2 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_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)