abstract_algebra
Definitions
Groups, Monoids, Semigroups, Quasigroups, Loops, & Magmas
Rings and Fields
Vector Spaces & Modules
Regular Representation
Abstract Matrices
Cayley-Dickson Construction
Resources
API Reference
License
abstract_algebra
Index
Index
_
|
A
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
U
|
V
|
W
|
X
|
Y
|
Z
_
_filter_out_conflicts() (in module finite_algebras)
_no_conflict() (in module finite_algebras)
_no_conflicts() (in module finite_algebras)
A
about() (cayley_table.CayleyTable method)
(finite_algebras.Examples method)
(finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Module method)
(finite_algebras.Monoid method)
(finite_algebras.NDimensionalModule method)
(finite_algebras.NDimensionalVectorSpace method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
(finite_algebras.VectorSpace method)
about_isomorphic_partition() (in module finite_algebras)
about_isomorphic_partitions() (in module finite_algebras)
about_subalgebras() (in module finite_algebras)
about_tables() (in module cayley_table)
AbstractMatrix (class in abstract_matrix)
add() (finite_algebras.Field method)
(finite_algebras.Ring method)
add_identity (finite_algebras.Field property)
(finite_algebras.Ring property)
add_s() (in module finite_algebras)
add_table (finite_algebras.Field property)
(finite_algebras.Ring property)
algebra (abstract_matrix.AbstractMatrix property)
(finite_algebras.Element property)
are_n() (in module finite_algebras)
array (abstract_matrix.AbstractMatrix property)
C
CayleyTable (class in cayley_table)
center() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
center_algebra() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
check_associativity() (in module finite_algebras)
check_dist_of_scalars_over_vec_add() (in module finite_algebras)
check_dist_of_vec_over_scalar_add() (in module finite_algebras)
check_module_conditions() (in module finite_algebras)
,
[1]
check_scaling_by_one() (in module finite_algebras)
closed_subsets_of_elements() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
closure() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
cofactor_matrix() (abstract_matrix.AbstractMatrix method)
commutator() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
commutator_subalgebra() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
commutators() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
conj() (finite_algebras.Field method)
(finite_algebras.Ring method)
conjugate() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
conjugates() (finite_algebras.Field method)
(finite_algebras.Ring method)
copy() (abstract_matrix.AbstractMatrix method)
copy_algebra() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
create_inverse_lookup_dict() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
D
delete_row_col() (in module finite_algebras)
determinant() (abstract_matrix.AbstractMatrix method)
dimensions (finite_algebras.NDimensionalModule property)
(finite_algebras.NDimensionalVectorSpace property)
direct_product_delimiter() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
distributes_over() (cayley_table.CayleyTable method)
div() (finite_algebras.Field method)
divisors() (in module my_math)
dot_product() (finite_algebras.NDimensionalModule method)
(finite_algebras.NDimensionalVectorSpace method)
dump() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
dumps() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
E
elem_conj() (finite_algebras.Field method)
(finite_algebras.Ring method)
Element (class in finite_algebras)
element_map() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
element_order() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
element_pairs_where_product_equals() (finite_algebras.Field method)
(finite_algebras.Ring method)
element_pairs_where_sum_equals() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
element_to_power() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
elements (finite_algebras.Field property)
(finite_algebras.FiniteAlgebra property)
(finite_algebras.Group property)
(finite_algebras.Loop property)
(finite_algebras.Magma property)
(finite_algebras.Monoid property)
(finite_algebras.Quasigroup property)
(finite_algebras.Ring property)
(finite_algebras.Semigroup property)
Examples (class in finite_algebras)
extract_additive_algebra() (finite_algebras.Field method)
(finite_algebras.Ring method)
extract_multiplicative_algebra() (finite_algebras.Field method)
(finite_algebras.Ring method)
F
Field (class in finite_algebras)
find_isomorphic_subalgebra() (in module finite_algebras)
FiniteAlgebra (class in finite_algebras)
FiniteCompositeAlgebra (class in finite_algebras)
FiniteOperator (class in finite_algebras)
G
generate_algebra_from_element_dict() (in module finite_algebras)
generate_algebra_mod_n() (in module finite_algebras)
generate_commutative_monoid() (in module finite_algebras)
generate_cyclic_group() (in module finite_algebras)
generate_nxn_matrix_algebra() (in module finite_algebras)
generate_powerset_group() (in module finite_algebras)
generate_powerset_ring() (in module finite_algebras)
generate_relative_primes_group() (in module finite_algebras)
generate_symmetric_group() (in module finite_algebras)
generates() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
generators() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
get_duplicates() (in module finite_algebras)
get_int_forms() (in module finite_algebras)
get_integer_form() (in module finite_algebras)
Group (class in finite_algebras)
H
has_cancellation() (cayley_table.CayleyTable method)
(finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
has_identity() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
has_inverses() (cayley_table.CayleyTable method)
(finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
has_mult_identity() (finite_algebras.Field method)
(finite_algebras.Ring method)
I
identity (finite_algebras.Field property)
(finite_algebras.FiniteAlgebra property)
(finite_algebras.Group property)
(finite_algebras.Loop property)
(finite_algebras.Magma property)
(finite_algebras.Monoid property)
(finite_algebras.Quasigroup property)
(finite_algebras.Ring property)
(finite_algebras.Semigroup property)
identity() (abstract_matrix.AbstractMatrix class method)
(cayley_table.CayleyTable method)
index_table_from_name_table() (in module finite_algebras)
InfixNotation (class in finite_algebras)
inv() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
inverse() (abstract_matrix.AbstractMatrix method)
inverse_lookup_dict() (cayley_table.CayleyTable method)
inverse_mapping() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
is_abelian() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_associative() (cayley_table.CayleyTable method)
(finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_commutative() (cayley_table.CayleyTable method)
(finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_cyclic() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_even (permutations.Perm property)
is_field() (in module finite_algebras)
is_gaussian_prime() (finite_algebras.Field method)
(finite_algebras.Ring method)
is_isomorphic_mapping() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_normal() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
is_regular() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
is_relatively_prime() (in module my_math)
is_table_associative() (in module finite_algebras)
isomorphic() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
L
left_cosets() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
left_identity() (cayley_table.CayleyTable method)
Loop (class in finite_algebras)
M
Magma (class in finite_algebras)
make_cayley_dickson_algebra() (finite_algebras.Field method)
(finite_algebras.Ring method)
make_cayley_table() (in module finite_algebras)
make_element_mappings() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
make_finite_algebra() (in module finite_algebras)
make_table_from_xml() (in module finite_algebras)
mapping (permutations.Perm property)
minor() (abstract_matrix.AbstractMatrix method)
minus_one (finite_algebras.Field property)
(finite_algebras.Ring property)
Module (class in finite_algebras)
module_dot_product() (in module finite_algebras)
,
[1]
module_sv_mult() (in module finite_algebras)
,
[1]
Monoid (class in finite_algebras)
mult() (finite_algebras.Field method)
(finite_algebras.Ring method)
mult_abelian_subgroup() (finite_algebras.Field method)
mult_identity (finite_algebras.Field property)
(finite_algebras.Ring property)
mult_inv() (finite_algebras.Field method)
mult_is_commutative() (finite_algebras.Field method)
(finite_algebras.Ring method)
mult_table (finite_algebras.Field property)
(finite_algebras.Ring property)
N
name (finite_algebras.Element property)
ncols (abstract_matrix.AbstractMatrix property)
NDimensionalModule (class in finite_algebras)
NDimensionalVectorSpace (class in finite_algebras)
norm() (finite_algebras.Field method)
(finite_algebras.Ring method)
np_arr_to_tuple() (in module finite_algebras)
nrows (abstract_matrix.AbstractMatrix property)
O
one (finite_algebras.Field property)
(finite_algebras.Ring property)
order (cayley_table.CayleyTable property)
(finite_algebras.Field property)
(finite_algebras.FiniteAlgebra property)
(finite_algebras.Group property)
(finite_algebras.Loop property)
(finite_algebras.Magma property)
(finite_algebras.Monoid property)
(finite_algebras.Quasigroup property)
(finite_algebras.Ring property)
(finite_algebras.Semigroup property)
origin (finite_algebras.NDimensionalModule property)
(finite_algebras.NDimensionalVectorSpace property)
P
parity (permutations.Perm property)
partition_into_isomorphic_lists() (in module finite_algebras)
Perm (class in permutations)
powerset() (in module finite_algebras)
proper_subalgebras() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
Q
Quasigroup (class in finite_algebras)
quotient_group() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
R
random() (abstract_matrix.AbstractMatrix class method)
regular_representation() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
relative_primes() (in module my_math)
reorder_elements() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
right_cosets() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
right_identity() (cayley_table.CayleyTable method)
ring (abstract_matrix.AbstractMatrix property)
Ring (class in finite_algebras)
S
same_lists_of_lists() (in module finite_algebras)
scalar_mult() (abstract_matrix.AbstractMatrix method)
(finite_algebras.Field method)
(finite_algebras.Ring method)
Semigroup (class in finite_algebras)
shape (abstract_matrix.AbstractMatrix property)
show() (permutations.Perm method)
size (permutations.Perm property)
split_element() (finite_algebras.Field method)
(finite_algebras.Ring method)
sqr() (finite_algebras.Field method)
(finite_algebras.Ring method)
square_root_mapping() (finite_algebras.Field method)
(finite_algebras.Ring method)
square_roots() (finite_algebras.Field method)
(finite_algebras.Ring method)
sub() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
subalgebra_from_elements() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
subgroups() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
symm_diff_of_two_lists_of_lists() (in module finite_algebras)
T
table (cayley_table.CayleyTable property)
(finite_algebras.Field property)
(finite_algebras.FiniteAlgebra property)
(finite_algebras.Group property)
(finite_algebras.Loop property)
(finite_algebras.Magma property)
(finite_algebras.Monoid property)
(finite_algebras.Quasigroup property)
(finite_algebras.Ring property)
(finite_algebras.Semigroup property)
table_entries_where_equal_to() (cayley_table.CayleyTable method)
tables_to_groups() (in module finite_algebras)
to_dict() (finite_algebras.Field method)
(finite_algebras.FiniteAlgebra method)
(finite_algebras.Group method)
(finite_algebras.Loop method)
(finite_algebras.Magma method)
(finite_algebras.Monoid method)
(finite_algebras.Quasigroup method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
to_list_with_names() (cayley_table.CayleyTable method)
to_tuple() (abstract_matrix.AbstractMatrix method)
tolist() (cayley_table.CayleyTable method)
totient() (in module my_math)
transpose() (abstract_matrix.AbstractMatrix method)
trivial_subgroups() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
type_of_algebra() (cayley_table.CayleyTable method)
U
unique_proper_subgroups() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Ring method)
units() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
units_subgroup() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
unpack_components() (in module finite_algebras)
V
vector_add() (finite_algebras.Module method)
(finite_algebras.NDimensionalModule method)
(finite_algebras.NDimensionalVectorSpace method)
(finite_algebras.VectorSpace method)
VectorSpace (class in finite_algebras)
verify_regular_representation() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
W
weak_inverses() (finite_algebras.Field method)
(finite_algebras.Group method)
(finite_algebras.Monoid method)
(finite_algebras.Ring method)
(finite_algebras.Semigroup method)
X
xgcd() (in module my_math)
Y
yes_or_no() (in module finite_algebras)
Z
zero (finite_algebras.Field property)
(finite_algebras.Ring property)
zero_divisor_pairs() (finite_algebras.Field method)
(finite_algebras.Ring method)
zero_divisors() (finite_algebras.Field method)
(finite_algebras.Ring method)
zeros() (abstract_matrix.AbstractMatrix class method)