Index

_

_add() (avisogenies_sage.theta_point.AbelianVarietyPoint method) (avisogenies_sage.theta_point.KummerVarietyPoint method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _add_() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _addition_formula() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) _char_to_idx() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint static method) _check() (avisogenies_sage.theta_point.KummerVarietyPoint method) _diff_add_PQ() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _diff_add_PQfactor() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _from_curve() (in module avisogenies_sage.constructor) _get_nonzero_coord() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _idx_to_char() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) _latex_() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _level (avisogenies_sage.theta_null_point.KummerVariety attribute)

_mult() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _neg_() (avisogenies_sage.theta_point.KummerVarietyPoint method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _point (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint attribute) (avisogenies_sage.theta_null_point.AbelianVariety_ThetaStructure attribute) (avisogenies_sage.theta_null_point.KummerVariety attribute) (avisogenies_sage.theta_null_point.Variety_ThetaStructure attribute) _point_homset() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) _repr_() (avisogenies_sage.theta_null_point.AbelianVariety_ThetaStructure method) (avisogenies_sage.theta_null_point.KummerVariety method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _rmul_() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) _root() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) _weierstrass_points() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) _with_theta_basis() (in module avisogenies_sage.constructor)

A

abelian_variety() (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint method) (avisogenies_sage.theta_point.AbelianVarietyPoint method) AbelianVariety() (in module avisogenies_sage.constructor) AbelianVariety_ThetaStructure (class in avisogenies_sage.theta_null_point) AbelianVarietyPoint (class in avisogenies_sage.theta_point) add_twotorsion_point() (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint method) AnalyticThetaNullPoint (class in avisogenies_sage.analytic_theta_point) AnalyticThetaPoint (class in avisogenies_sage.analytic_theta_point) avisogenies_sage.analytic_theta_point module avisogenies_sage.aux_hyper module avisogenies_sage.constructor module avisogenies_sage.ep_elements module

avisogenies_sage.eta_maps module avisogenies_sage.morphisms_aux module avisogenies_sage.morphisms_level2 module avisogenies_sage.morphisms_level4 module avisogenies_sage.theta_null_point module avisogenies_sage.theta_point module avisogenies_sage.tools module

B

base_extend() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method)

C

change_ring() (avisogenies_sage.theta_null_point.AbelianVariety_ThetaStructure method) (avisogenies_sage.theta_null_point.KummerVariety method) (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) choice_of_all_C_Cosset() (in module avisogenies_sage.morphisms_aux) choice_of_C_Cosset() (in module avisogenies_sage.morphisms_aux) clean_common() (avisogenies_sage.ep_elements.EpElement method)

compatible_lift() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) compatible_sqrt() (in module avisogenies_sage.morphisms_aux) constant_f() (in module avisogenies_sage.morphisms_aux) constant_f2_level2() (in module avisogenies_sage.morphisms_aux) create_conversions() (in module avisogenies_sage.tools) create_indexing() (in module avisogenies_sage.tools) curve() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method)

D

diff_add() (avisogenies_sage.theta_point.AbelianVarietyPoint method) (avisogenies_sage.theta_point.KummerVarietyPoint method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method)

diff_multadd() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) dimension() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) (avisogenies_sage.theta_null_point.Variety_ThetaStructure method)

E

e_2() (in module avisogenies_sage.eta_maps) e_star() (in module avisogenies_sage.eta_maps) EpElement (class in avisogenies_sage.ep_elements) equations() (avisogenies_sage.theta_null_point.AbelianVariety_ThetaStructure method) (avisogenies_sage.theta_null_point.KummerVariety method)

eta() (in module avisogenies_sage.eta_maps) eta_prime() (in module avisogenies_sage.eta_maps) eta_second() (in module avisogenies_sage.eta_maps) eval_car() (in module avisogenies_sage.tools) evaluate() (avisogenies_sage.ep_elements.EpElement method) evaluate_formal_points() (in module avisogenies_sage.tools)

F

from_algebraic() (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint class method)

from_curve() (avisogenies_sage.theta_null_point.KummerVariety method) from_divisor() (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint class method)

G

get_dual_quadruplet() (in module avisogenies_sage.tools)

I

idx() (in module avisogenies_sage.tools) IgusaTheorem() (in module avisogenies_sage.morphisms_aux)

is_equal() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) isogeny() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method)

K

kummer_variety() (avisogenies_sage.theta_point.KummerVarietyPoint method)

KummerVariety (class in avisogenies_sage.theta_null_point) KummerVarietyPoint (class in avisogenies_sage.theta_point)

L

level() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint method) (avisogenies_sage.theta_null_point.Variety_ThetaStructure method)

Level2ThetaPointToMumford() (in module avisogenies_sage.morphisms_level2) Level4ThetaPointToMumford() (in module avisogenies_sage.morphisms_level4)

M

module avisogenies_sage.analytic_theta_point avisogenies_sage.aux_hyper avisogenies_sage.constructor avisogenies_sage.ep_elements avisogenies_sage.eta_maps avisogenies_sage.morphisms_aux avisogenies_sage.morphisms_level2 avisogenies_sage.morphisms_level4 avisogenies_sage.theta_null_point avisogenies_sage.theta_point avisogenies_sage.tools

MumfordToLevel2ThetaPoint() (in module avisogenies_sage.morphisms_level2) MumfordToLevel4ThetaPoint() (in module avisogenies_sage.morphisms_level4) MumfordToTheta_2_Generic() (in module avisogenies_sage.morphisms_level2) MumfordToTheta_4_Generic() (in module avisogenies_sage.morphisms_level4)

N

normalize_eta() (in module avisogenies_sage.eta_maps)

P

point() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) (avisogenies_sage.theta_null_point.Variety_ThetaStructure method)

prodYp_fromMumford_with2torsion() (in module avisogenies_sage.morphisms_aux)

R

rangeS() (in module avisogenies_sage.tools) reduce_sym() (in module avisogenies_sage.tools) reduce_symcouple() (in module avisogenies_sage.tools) reduce_symtwotorsion() (in module avisogenies_sage.tools) reduce_symtwotorsion_couple() (in module avisogenies_sage.tools)

reduce_twotorsion() (in module avisogenies_sage.tools) reduce_twotorsion_couple() (in module avisogenies_sage.tools) remove_h() (in module avisogenies_sage.aux_hyper) riemann_relation() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) rosenhain_model() (in module avisogenies_sage.aux_hyper)

S

scale() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) scheme() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method)

sign_s_A() (in module avisogenies_sage.morphisms_aux) sign_theta_normalized() (in module avisogenies_sage.eta_maps)

T

tate_pairing() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) theta_null_point() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) ThetaToMumford_2_algclose() (in module avisogenies_sage.morphisms_level2) ThetaToMumford_2_Generic() (in module avisogenies_sage.morphisms_level2)

ThetaToMumford_4_Generic() (in module avisogenies_sage.morphisms_level4) three_way_add() (avisogenies_sage.theta_point.VarietyThetaStructurePoint method) to_algebraic() (avisogenies_sage.analytic_theta_point.AnalyticThetaNullPoint method) (avisogenies_sage.analytic_theta_point.AnalyticThetaPoint method) transformation() (in module avisogenies_sage.aux_hyper)

V

Variety_ThetaStructure (class in avisogenies_sage.theta_null_point)

VarietyThetaStructurePoint (class in avisogenies_sage.theta_point)

W

weil_pairing() (avisogenies_sage.theta_point.KummerVarietyPoint method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method)

with_theta_basis() (avisogenies_sage.theta_null_point.Variety_ThetaStructure method) (avisogenies_sage.theta_point.VarietyThetaStructurePoint method)

Y

Y_fromMumford_with2torsion() (in module avisogenies_sage.morphisms_aux) Ylm_fromTheta() (in module avisogenies_sage.morphisms_level4)

YS_fromMumford_Delta() (in module avisogenies_sage.morphisms_aux) YS_fromMumford_Generic() (in module avisogenies_sage.morphisms_aux)