Index
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
K
|
L
|
M
|
N
|
O
|
P
|
R
|
S
|
T
|
U
|
W
A
AbelianGroupHomomorphism (class in dual_pairs.abelian_group_homomorphism)
AbelianSheaf (class in dual_pairs.abelian_sheaf)
add() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.torsor_pair.TorsorPair method)
algebra() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
(dual_pairs.torsor_pair.TorsorPair method)
algebra1() (dual_pairs.dual_pair.DualPair_class method)
algebra2() (dual_pairs.dual_pair.DualPair_class method)
algebra_and_points_from_action() (in module dual_pairs.dual_pair_from_table)
algebra_element() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_generic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_monogenic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_product method)
artin_conductor() (dual_pairs.dual_pair.DualPair_class method)
automorphism_matrix() (dual_pairs.dual_pair.DualPair_class method)
B
basis() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
C
change_ring() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
(dual_pairs.finite_flat_algebra_module.FiniteFlatAlgebraModule method)
class_group() (in module dual_pairs.class_group)
cokernel() (dual_pairs.abelian_group_homomorphism.AbelianGroupHomomorphism method)
commutative_subgroup() (dual_pairs.ext_group.ExtGroup method)
conductor_exponent() (dual_pairs.dual_pair.DualPair_class method)
contracted_product() (dual_pairs.torsor_pair.TorsorPair method)
counit1() (dual_pairs.dual_pair.DualPair_class method)
counit2() (dual_pairs.dual_pair.DualPair_class method)
create_key() (dual_pairs.dual_pair.DualPairFactory method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebraFactory method)
create_object() (dual_pairs.dual_pair.DualPairFactory method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebraFactory method)
D
degree() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
dirichlet_character() (dual_pairs.dual_pair_rational.DualPair_rational method)
discriminant() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
dual() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.finite_flat_algebra_module.FiniteFlatAlgebraModule method)
dual_module() (dual_pairs.torsor_pair.TorsorPair method)
dual_pair() (dual_pairs.torsor_pair.TorsorPair method)
dual_pair_from_dihedral_field() (in module dual_pairs.dual_pair_from_dihedral_field)
dual_pair_from_table() (in module dual_pairs.dual_pair_from_table)
dual_pair_import() (in module dual_pairs.dual_pair_import)
dual_pairs.abelian_group_homomorphism
module
dual_pairs.abelian_sheaf
module
dual_pairs.class_group
module
dual_pairs.dual_pair
module
dual_pairs.dual_pair_from_dihedral_field
module
dual_pairs.dual_pair_from_table
module
dual_pairs.dual_pair_import
module
dual_pairs.dual_pair_rational
module
dual_pairs.ext_group
module
dual_pairs.extension
module
dual_pairs.finite_flat_algebra
module
dual_pairs.finite_flat_algebra_element
module
dual_pairs.finite_flat_algebra_module
module
dual_pairs.group_structure
module
dual_pairs.padic_roots
module
dual_pairs.selmer_group
module
dual_pairs.simplicial_sheaf
module
dual_pairs.smith_form
module
dual_pairs.torsor_class_group
module
dual_pairs.torsor_pair
module
dual_pairs.unit_group
module
dual_points() (dual_pairs.dual_pair.DualPair_class method)
DualPair_class (class in dual_pairs.dual_pair)
DualPair_rational (class in dual_pairs.dual_pair_rational)
DualPairFactory (class in dual_pairs.dual_pair)
E
Element (dual_pairs.ext_group.ExtGroup attribute)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic attribute)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic attribute)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product attribute)
(dual_pairs.finite_flat_algebra_module.FiniteFlatAlgebraModule attribute)
(dual_pairs.torsor_class_group.TorsorClassGroup attribute)
extension() (in module dual_pairs.extension)
ExtGroup (class in dual_pairs.ext_group)
ExtGroup_mu_n() (in module dual_pairs.ext_group)
ExtGroupElement (class in dual_pairs.ext_group)
ExtGroupGm() (in module dual_pairs.ext_group)
F
find_group_structure() (in module dual_pairs.group_structure)
find_group_structure_old() (in module dual_pairs.group_structure)
find_perm() (in module dual_pairs.group_structure)
finite_dimensional_algebra() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
FiniteFlatAlgebra_base (class in dual_pairs.finite_flat_algebra)
FiniteFlatAlgebra_generic (class in dual_pairs.finite_flat_algebra)
FiniteFlatAlgebra_monogenic (class in dual_pairs.finite_flat_algebra)
FiniteFlatAlgebra_product (class in dual_pairs.finite_flat_algebra)
FiniteFlatAlgebraElement (class in dual_pairs.finite_flat_algebra_element)
FiniteFlatAlgebraElement_generic (class in dual_pairs.finite_flat_algebra_element)
FiniteFlatAlgebraElement_monogenic (class in dual_pairs.finite_flat_algebra_element)
FiniteFlatAlgebraElement_product (class in dual_pairs.finite_flat_algebra_element)
FiniteFlatAlgebraFactory (class in dual_pairs.finite_flat_algebra)
FiniteFlatAlgebraModule (class in dual_pairs.finite_flat_algebra_module)
FiniteFlatAlgebraModuleElement (class in dual_pairs.finite_flat_algebra_module)
frobenius_charpoly() (dual_pairs.dual_pair.DualPair_class method)
frobenius_matrix() (dual_pairs.dual_pair.DualPair_class method)
frobenius_traces() (dual_pairs.dual_pair_rational.DualPair_rational method)
G
gen() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
gens() (dual_pairs.ext_group.ExtGroup method)
(dual_pairs.torsor_class_group.TorsorClassGroup method)
gens_orders() (dual_pairs.ext_group.ExtGroup method)
(dual_pairs.torsor_class_group.TorsorClassGroup method)
group_structure() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.ext_group.ExtGroup method)
(dual_pairs.torsor_class_group.TorsorClassGroup method)
group_structure_algebraic_closure() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.dual_pair_rational.DualPair_rational method)
H
homology() (in module dual_pairs.abelian_group_homomorphism)
hopf_algebra() (dual_pairs.dual_pair.DualPair_class method)
I
integral_basis_generator() (in module dual_pairs.padic_roots)
inverse_image() (dual_pairs.abelian_group_homomorphism.AbelianGroupHomomorphism method)
inverse_of_unit() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement method)
is_commutative() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
is_field() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
is_isomorphic() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.torsor_pair.TorsorPair method)
is_trivial() (dual_pairs.torsor_pair.TorsorPair method)
is_unit() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement method)
is_valid() (dual_pairs.dual_pair.DualPair_class method)
isom_torsor() (dual_pairs.torsor_pair.TorsorPair method)
K
kernel() (dual_pairs.abelian_group_homomorphism.AbelianGroupHomomorphism method)
kummer_dedekind() (in module dual_pairs.padic_roots)
L
lift_root() (in module dual_pairs.padic_roots)
lift_to_prime() (in module dual_pairs.dual_pair_rational)
M
matrix() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_generic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_monogenic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_product method)
mod1() (in module dual_pairs.group_structure)
module
dual_pairs.abelian_group_homomorphism
dual_pairs.abelian_sheaf
dual_pairs.class_group
dual_pairs.dual_pair
dual_pairs.dual_pair_from_dihedral_field
dual_pairs.dual_pair_from_table
dual_pairs.dual_pair_import
dual_pairs.dual_pair_rational
dual_pairs.ext_group
dual_pairs.extension
dual_pairs.finite_flat_algebra
dual_pairs.finite_flat_algebra_element
dual_pairs.finite_flat_algebra_module
dual_pairs.group_structure
dual_pairs.padic_roots
dual_pairs.selmer_group
dual_pairs.simplicial_sheaf
dual_pairs.smith_form
dual_pairs.torsor_class_group
dual_pairs.torsor_pair
dual_pairs.unit_group
module() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
module_element() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_generic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_monogenic method)
(dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement_product method)
(dual_pairs.finite_flat_algebra_module.FiniteFlatAlgebraModuleElement method)
monomial_coefficients() (dual_pairs.finite_flat_algebra_element.FiniteFlatAlgebraElement method)
morphisms_to_ring() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
multiplication_by_m() (dual_pairs.dual_pair.DualPair_class method)
multiplication_tensor() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
MultiplicativeGroup (class in dual_pairs.abelian_sheaf)
N
ngens() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
O
one() (dual_pairs.ext_group.ExtGroup method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
(dual_pairs.torsor_class_group.TorsorClassGroup method)
opposite() (dual_pairs.torsor_pair.TorsorPair method)
order() (dual_pairs.ext_group.ExtGroup method)
(dual_pairs.torsor_class_group.TorsorClassGroup method)
P
padic_aut() (in module dual_pairs.padic_roots)
padic_roots() (in module dual_pairs.padic_roots)
pairing() (dual_pairs.dual_pair.DualPair_class method)
phi() (dual_pairs.dual_pair.DualPair_class method)
points() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.torsor_pair.TorsorPair method)
psi() (dual_pairs.torsor_pair.TorsorPair method)
R
ramified_primes() (dual_pairs.dual_pair_rational.DualPair_rational method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
random_element() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
(dual_pairs.finite_flat_algebra_module.FiniteFlatAlgebraModule method)
reduce_element() (in module dual_pairs.padic_roots)
reduce_poly() (in module dual_pairs.padic_roots)
representation_table() (dual_pairs.dual_pair.DualPair_class method)
rootpadic() (in module dual_pairs.padic_roots)
roots_mod_m() (in module dual_pairs.padic_roots)
roots_of_unity() (in module dual_pairs.unit_group)
RootsOfUnity (class in dual_pairs.abelian_sheaf)
S
selmer_group() (in module dual_pairs.selmer_group)
SimplicialSheaf (class in dual_pairs.simplicial_sheaf)
solve_left() (dual_pairs.abelian_group_homomorphism.AbelianGroupHomomorphism method)
solve_mod() (in module dual_pairs.abelian_group_homomorphism)
solve_mod_right() (in module dual_pairs.abelian_group_homomorphism)
solve_right() (dual_pairs.abelian_group_homomorphism.AbelianGroupHomomorphism method)
some_elements() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
splitting_field() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.dual_pair_rational.DualPair_rational method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_generic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_monogenic method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_product method)
(dual_pairs.torsor_pair.TorsorPair method)
splitting_field_polynomial() (dual_pairs.dual_pair.DualPair_class method)
(dual_pairs.dual_pair_rational.DualPair_rational method)
(dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
standard_group_structure() (in module dual_pairs.group_structure)
T
tensor_product() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
theta() (dual_pairs.dual_pair.DualPair_class method)
to_generic() (dual_pairs.finite_flat_algebra.FiniteFlatAlgebra_base method)
Torsor (class in dual_pairs.torsor_class_group)
torsor_class_group() (dual_pairs.dual_pair_rational.DualPair_rational method)
torsor_pair() (dual_pairs.torsor_class_group.Torsor method)
TorsorClassGroup (class in dual_pairs.torsor_class_group)
TorsorPair (class in dual_pairs.torsor_pair)
trivial_torsor() (dual_pairs.dual_pair.DualPair_class method)
U
unit1() (dual_pairs.dual_pair.DualPair_class method)
unit2() (dual_pairs.dual_pair.DualPair_class method)
unit_group() (in module dual_pairs.unit_group)
upsilon() (dual_pairs.torsor_pair.TorsorPair method)
W
weight() (dual_pairs.dual_pair.DualPair_class method)
Dual pairs of algebras
Navigation
Dual pairs of algebras
Constructing a dual pair of algebras from a dihedral field
Constructing a dual pair of algebras from a table
Importing a dual pair of algebras from a file
Dual pairs of algebras over the rationals
Finite flat algebras
Elements of finite flat algebras
Modules over finite flat algebras
Class groups of finite flat algebras
Unit groups of finite flat algebras
Selmer groups of finite flat algebras
Extension class groups
Torsor class groups
Torsor modules
Sheaves of Abelian groups
Simplicial sheaves
Homomorphisms of finitely generated Abelian groups
Example: easy extensions
Utility functions for finite Abelian groups
Utility functions for
p
-adic polynomials
Smith normal form for Abelian groups
Related Topics
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