AVIsogenies
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Documentation
Varieties with theta structure
Theta points
Analytic theta null point
Ep elements
Eta maps
Morphisms
Auxiliary functions
Tutorials
A tutorial on how to use AVIsogenies in SageMath
AVIsogenies
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Index
Index
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A
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B
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C
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D
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E
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F
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G
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I
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K
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L
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M
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N
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P
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R
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S
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T
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V
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W
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Y
_
_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)