Index

A

a_CM_type() (recip.cm_types.CM_Field_absolute method) a_to_mu() (in module recip.find_class_invariant) ABCD() (in module recip.symplectic_matrices) abs_to_rel() (recip.cm_types.CM_Field_absolute method)

action_on_theta_generators() (recip.symplectic_matrices.GSp_element method) additive_gens_to_basis() (in module recip.orders) all_period_matrices_two() (in module recip.bissonstreng) are_nn_isogenous() (in module recip.orders)

B

base_ring() (recip.symplectic_matrices.GSp_element method) basis() (recip.period_matrices.PeriodMatrix_CM method)

bruinier_yang_applies() (in module recip.denominators) bruinier_yang_bound() (in module recip.denominators)

C

c_to_num() (in module recip.theta_trans) calI() (in module recip.denominators) calIp() (in module recip.denominators) calIp_enumerate() (in module recip.denominators) calIp_fast() (in module recip.denominators) calJ_bound() (in module recip.denominators) calJ_bound_thm24() (in module recip.denominators) calJ_conjecture() (in module recip.denominators) change_den() (recip.theta_trans.Theta_element_polynomial_ring method) class_group_iter() (recip.cm_types.CM_Field_absolute method) class_polynomials() (in module recip.class_polynomials) class_polynomials_order() (in module recip.orders) CM_Field() (in module recip.cm_types) CM_field() (recip.period_matrices.PeriodMatrix_CM method) CM_Field_absolute (class in recip.cm_types) CM_Field_quartic (class in recip.cm_types) CM_Type() (in module recip.cm_types) CM_type() (recip.period_matrices.PeriodMatrix_CM method) CM_Type_base (class in recip.cm_types) CM_Type_embeddings (class in recip.cm_types) CM_Type_quartic (class in recip.cm_types)

CM_type_to_mus() (in module recip.bissonstreng) CM_Type_xi (class in recip.cm_types) CM_types() (recip.cm_types.CM_Field_absolute method) (recip.cm_types.CM_Field_quartic method) codomain() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method) complex_conjugate() (recip.cm_types.CM_Type_quartic method) (recip.period_matrices.PeriodMatrix_CM method) complex_conjugation() (recip.cm_types.CM_Field_absolute method) complex_conjugation_symplectic_matrix() (recip.period_matrices.PeriodMatrix_CM method) complex_matrix() (recip.period_matrices.PeriodMatrix_CM method) conductor() (in module recip.denominators) cosets_of_GammaN_iter() (in module recip.bls) count_ideals() (in module recip.denominators) count_ideals1() (in module recip.denominators) count_ideals2() (in module recip.denominators) count_ideals3() (in module recip.denominators) count_nn_endomorphisms() (in module recip.bls) cycl_galois_action() (in module recip.theta_trans) cycl_galois_action_on_polynomials() (in module recip.theta_trans)

D

DAB() (recip.cm_types.CM_Field_quartic method) DAB_to_minimal() (in module recip.cm_types) DAm_to_DAB() (in module recip.list_fields) den_weight() (recip.theta_trans.Theta_element_polynomial_ring method) denominator_bound() (in module recip.denominators)

determine_kappa() (in module recip.theta_trans) diag() (in module recip.symplectic_matrices) domain() (recip.cm_types.CM_Type_base method) (recip.cm_types.CM_Type_quartic method) dup_data() (in module recip.theta_trans) dup_formula() (in module recip.theta_trans)

E

Element (recip.theta_trans.ThetaGroup attribute) (recip.theta_trans.ThetaRing attribute) embed() (recip.cm_types.CM_Field_absolute method) embedding() (recip.cm_types.CM_Field_absolute method) embeddings() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method)

epsilon() (recip.period_matrices.PeriodMatrix_CM method) evaluate_theta() (in module recip.period_matrices) (recip.period_matrices.PeriodMatrix_CM method) evaluate_theta_interval() (in module recip.period_matrices) even_theta_characteristics() (in module recip.theta_trans)

F

find_eta() (in module recip.denominators) find_eta_coprime() (in module recip.denominators)

find_eta_pid() (in module recip.denominators) find_eta_pid_old() (in module recip.denominators)

G

g() (recip.cm_types.CM_Field_absolute method) (recip.cm_types.CM_Field_quartic method) (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method) (recip.period_matrices.PeriodMatrix_CM method) (recip.symplectic_matrices.GSp_element method) (recip.theta_trans.ThetaProduct method) g_reflex() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method)

galois_action() (recip.period_matrices.PeriodMatrix_CM method) galois_closure() (recip.cm_types.CM_Field_absolute method) goren_lauter_bound() (in module recip.denominators) gottschling_matrices() (in module recip.period_matrices) group_generators_to_list() (in module recip.symplectic_matrices) GSp_element (class in recip.symplectic_matrices) GSp_group (class in recip.symplectic_matrices)

H

h6_thesis() (in module recip.igusa_invariants) has_real_moduli() (recip.period_matrices.PeriodMatrix_CM method)

highest_root() (in module recip.cm_types) hilbert_symbol_trivial_outside() (in module recip.denominators) humbert8() (in module recip.bls)

I

ic_from_Cab() (in module recip.bls) ic_on_humb8() (in module recip.bls) ideal() (recip.period_matrices.PeriodMatrix_CM method) ideal_contains() (in module recip.orders) ideal_divide() (in module recip.orders) ideal_index() (in module recip.orders) ideal_inverse() (in module recip.orders) ideal_is_invertible() (in module recip.orders) ideal_order() (in module recip.orders) ideal_power() (in module recip.bls) ideals_equal() (in module recip.orders) igusa_absolute_to_homogeneous() (in module recip.igusa_invariants) igusa_homogeneous_to_absolute() (in module recip.igusa_invariants) igusa_invariants_absolute() (in module recip.igusa_invariants) igusa_modular_forms() (in module recip.igusa_invariants) igusa_modular_forms_to_absolute() (in module recip.igusa_invariants) intersect_ideals() (in module recip.orders) inverse_field_hom() (in module recip.cm_types) is_abelian() (recip.theta_trans.ThetaGroup method) is_D4() (recip.cm_types.CM_Field_quartic method) is_den_even() (in module recip.theta_trans)

is_finite() (recip.theta_trans.ThetaGroup method) is_fixed_by() (recip.theta_trans.Theta_element_polynomial_ring method) is_ideal() (in module recip.orders) is_period_matrix() (in module recip.period_matrices) is_polarized_product() (in module recip.bls) is_positive_definite() (in module recip.period_matrices) is_power_of_theta() (recip.theta_trans.Theta_element_polynomial_ring method) is_S_O_equal_S_OK() (in module recip.bissonstreng) is_symplectic() (in module recip.period_matrices) is_totally_imaginary_element() (recip.cm_types.CM_Field_absolute method) (recip.cm_types.CM_Field_quartic method) is_totally_positive_imaginary() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method) is_totally_positive_real_element() (recip.cm_types.CM_Field_absolute method) is_totally_real() (recip.cm_types.CM_Field_quartic method) is_totally_real_element() (recip.cm_types.CM_Field_absolute method) is_totally_real_positive() (recip.cm_types.CM_Field_quartic method) is_trivial_in_shimura_group() (in module recip.orders) iterate_DAB() (in module recip.list_fields) iterate_DAB_given_D() (in module recip.list_fields) iterate_DAB_given_DA() (in module recip.list_fields)

J

j_from_a() (in module recip.bls)

j_from_Cab() (in module recip.bls)

K

kappa() (in module recip.theta_trans)

L

lauter_viray_bound() (in module recip.denominators) lauter_viray_bound_given_eta() (in module recip.denominators) lauter_viray_win() (in module recip.denominators) level() (recip.theta_trans.ThetaProduct method) lift_ray_class_group_element() (in module recip.period_matrices)

lift_small() (in module recip.basic) list() (recip.symplectic_matrices.GSp_group method) (recip.symplectic_matrices.Sp_group method) list_group() (in module recip.find_class_invariant) long_name() (recip.theta_trans.Theta_element_polynomial_ring method) lower_root() (in module recip.bls)

M

make_big_zero() (in module recip.find_class_invariant) make_theta_ring() (in module recip.theta_trans) make_zero_big() (in module recip.find_class_invariant) mat_convert() (in module recip.basic) matrix() (recip.symplectic_matrices.GSp_element method) matrix_from_blocks() (in module recip.symplectic_matrices) minimal_DAB() (recip.cm_types.CM_Field_absolute method) minimal_F() (in module recip.orders) minimal_generating_subset() (in module recip.symplectic_matrices)

minimal_order_cl_nr_one_F() (in module recip.bissonstreng) minimal_orders_of_class_number_one() (in module recip.bissonstreng) mult_ic() (in module recip.bls) mult_ideals() (in module recip.orders) multiplication_formula() (recip.theta_trans.Theta_element_polynomial_ring method) my_ceil() (in module recip.period_matrices) my_floor() (in module recip.period_matrices) my_round() (in module recip.polynomials) my_sum() (in module recip.theta_trans)

N

name_to_den() (in module recip.theta_trans) name_to_den_c() (in module recip.theta_trans) negative_inverse() (recip.period_matrices.PeriodMatrix_CM method) next_prime_in_class() (in module recip.denominators) nn_isogenous_matrices_iter() (in module recip.bls)

nn_isogenous_matrices_iter2() (in module recip.bls) nu() (in module recip.symplectic_matrices) (recip.symplectic_matrices.GSp_element method) num_to_c() (in module recip.theta_trans) num_weight() (recip.theta_trans.Theta_element_polynomial_ring method)

O

Omega() (in module recip.symplectic_matrices) one_period_matrix() (recip.cm_types.CM_Field_absolute method) orbit() (recip.theta_trans.Theta_element method)

order() (recip.symplectic_matrices.GSp_group method) (recip.symplectic_matrices.Sp_group method) (recip.theta_trans.ThetaGroup method) orders_proven_with_wamelen() (in module recip.bissonstreng)

P

parent() (recip.symplectic_matrices.GSp_element method) period_matrices() (in module recip.orders) period_matrices_iter() (recip.cm_types.CM_Field_absolute method) PeriodMatrix() (in module recip.period_matrices)

PeriodMatrix_CM (class in recip.period_matrices) Phi() (recip.cm_types.CM_Field_quartic method) polarized_ideal_classes() (in module recip.orders) principal_type_norms() (in module recip.find_class_invariant) proper_ideal_classes() (in module recip.orders)

R

random_period_matrix() (in module recip.period_matrices) random_symplectic_matrix() (in module recip.symplectic_matrices) rational_function() (recip.theta_trans.Theta_element_polynomial_ring method) real_field() (recip.cm_types.CM_Field_absolute method) real_generator_in_self() (recip.cm_types.CM_Field_absolute method) real_to_self() (recip.cm_types.CM_Field_absolute method) recip.basic (module) recip.bissonstreng (module) recip.bls (module) recip.class_polynomials (module) recip.cm_types (module) recip.denominators (module) recip.find_class_invariant (module) recip.igusa_invariants (module) recip.list_fields (module) recip.orders (module) recip.period_matrices (module) recip.polynomials (module) recip.symplectic_matrices (module) recip.theta_trans (module) reciprocity_map_image() (in module recip.find_class_invariant)

recognize_all_from_article() (in module recip.bls) recognize_matrix() (in module recip.bls) recognize_polynomial() (in module recip.polynomials) reduce() (recip.period_matrices.PeriodMatrix_CM method) reduce_ic() (in module recip.bls) reflex() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_xi method) reflex_field() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method) (recip.period_matrices.PeriodMatrix_CM method) reflex_to_codomain() (recip.cm_types.CM_Type_embeddings method) (recip.cm_types.CM_Type_quartic method) (recip.cm_types.CM_Type_xi method) rel_to_self() (recip.cm_types.CM_Field_absolute method) relative_different() (recip.cm_types.CM_Field_absolute method) relative_field() (recip.cm_types.CM_Field_absolute method) relative_norm() (recip.cm_types.CM_Field_absolute method) relative_trace() (recip.cm_types.CM_Field_absolute method) rhotilde() (in module recip.denominators) rosenhain_invariants() (in module recip.igusa_invariants)

S

self_to_real() (recip.cm_types.CM_Field_absolute method) self_to_rel() (recip.cm_types.CM_Field_absolute method) Shimura_reciprocity() (recip.period_matrices.PeriodMatrix_CM method) short_interpolation() (in module recip.polynomials) Sp_action() (in module recip.period_matrices) (recip.period_matrices.PeriodMatrix_CM method)

Sp_group (class in recip.symplectic_matrices) Sp_part() (recip.symplectic_matrices.GSp_element method) sq_brackets_inverse() (in module recip.theta_trans) subscript_zero() (in module recip.theta_trans) superorders() (in module recip.orders) superorders_stable_under_complex_conjugation() (in module recip.orders) symplectic_generators() (in module recip.symplectic_matrices)

T

table() (in module recip.find_class_invariant) Theta (in module recip.theta_trans) theta_action_without_kappa() (in module recip.theta_trans) theta_c_mod_Z() (in module recip.theta_trans) Theta_element (class in recip.theta_trans) Theta_element_polynomial_ring (class in recip.theta_trans) theta_lc_complex() (in module recip.theta_trans) theta_lc_cyclotomic() (in module recip.theta_trans) theta_leading_term_complex() (in module recip.theta_trans) theta_leading_term_cyclotomic() (in module recip.theta_trans) theta_ring() (in module recip.theta_trans)

theta_ring_inclusion() (in module recip.theta_trans) theta_trans_k() (in module recip.theta_trans) ThetaGroup (class in recip.theta_trans) ThetaModForm() (in module recip.theta_trans) ThetaProduct (class in recip.theta_trans) ThetaRing (class in recip.theta_trans) ThetaSum (class in recip.theta_trans) trace_dual_complex_conjugate() (in module recip.orders) transpose() (recip.symplectic_matrices.GSp_element method) two_two_matrix() (in module recip.bissonstreng) type_norm() (recip.cm_types.CM_Type_base method) type_trace() (recip.cm_types.CM_Type_quartic method)

U

uniformizer() (in module recip.basic)

V

visualize() (in module recip.find_class_invariant)

visualize_orders() (in module recip.bissonstreng)

W

wamelen_curves() (in module recip.list_fields) wamelen_dab_list() (in module recip.list_fields)

weight() (recip.theta_trans.Theta_element_polynomial_ring method) (recip.theta_trans.ThetaProduct method) win_implementation() (in module recip.denominators)

X

xi() (recip.cm_types.CM_Type_xi method) (recip.period_matrices.PeriodMatrix_CM method)

Z

zero_matrix() (in module recip.symplectic_matrices)

Zmod_to_SL() (in module recip.symplectic_matrices)