group
numqi.group.cayley_table_to_left_regular_form(index_tuple)
Cayley table to left regular form
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
index_tuple
|
tuple
|
2-dimensional tuple, np.ndarray shape=(N0,N0) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(N0,N0,N0), np.int64 |
numqi.group.get_klein_four_group_cayley_table()
Klein four group Cayley table
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(4,4), np.int64 |
numqi.group.get_dihedral_group_cayley_table(n)
Dihedral group Cayley table stackexchange-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
n
|
int
|
n>=3, number of vertices |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(2n,2n), np.int64 |
numqi.group.get_cyclic_group_cayley_table(n)
Cyclic group Cayley table
cyclic group irrep on C-field is just complex number, on R-field are 2-by-2 matrix
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
n
|
int
|
n>=2, order of the group |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(n,n), np.int64 |
numqi.group.get_multiplicative_group_cayley_table(n)
Multiplicative group Cayley table, direct product of cyclic group wiki-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
n
|
int
|
n>=3 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(n,n), np.int64 |
numqi.group.get_quaternion_cayley_table()
Quaternion group Cayley table
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(8,8), np.int64 |
numqi.group.reduce_group_representation(np0, zero_eps=1e-07, tagI=False)
Reduce group representation to irreducible representations sheaves-blog
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np0
|
ndarray
|
shape=(N0,dim,dim) |
required |
zero_eps
|
float
|
zero threshold |
1e-07
|
tagI
|
bool
|
tag to indicate whether contain identity representation, if True, put at the first position |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
list
|
list of np.ndarray, shape=(N0,dim_irrep,dim_irrep) |
numqi.group.to_unitary_representation(np0, return_matP=False)
To unitary representation
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np0
|
ndarray
|
shape=(N0,dim,dim) |
required |
return_matP
|
bool
|
return matP |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(N0,dim,dim), unitary representation |
matP |
ndarray
|
when |
numqi.group.matrix_block_diagonal(*np_list)
Matrix block diagonal, matrix direct sum
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
np_list
|
list
|
list of np.ndarray, shape=(N0,...,dim0,dim1) |
()
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
ndarray
|
shape=(N0,...,sum(dim0),sum(dim1)) |
numqi.group.get_character_and_class(irrep_list, zero_eps=1e-07, tagIFirst=False)
get character table and conjugacy class from irredicible representation
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
irrep_list
|
list
|
list of np.ndarray, shape=(N0,dim_irrep,dim_irrep) |
required |
zero_eps
|
float
|
zero threshold |
1e-07
|
tagIFirst
|
bool
|
if True, put the identity class at the first column |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
character |
ndarray
|
shape=(N0,N0), np.complex128 |
class_list |
list
|
list of tuple, tuple of int |
character_table |
ndarray
|
shape=(len(irrep),len(irrep)), np.complex128 |
numqi.group.hf_Euler_totient(n)
Euler's totient function stackoverflow-link
TODO sympy.totient()
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
n
|
int
|
n>=1 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
int
|
number of positive integers less than n that are coprime to n |
numqi.group.hf_is_prime(n)
Is prime number stackoverflow-link
True: 2,3,5,7
False: -1,0,1,4,6
TODO sympy.isprime()
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
n
|
int
|
n>=2 |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
bool
|
True if n is prime number |
numqi.group.pretty_print_character_table(character_table, class_list)
Pretty print character table
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
character_table
|
ndarray
|
shape=(len(irrep),len(irrep)), np.complex128 |
required |
class_list
|
list
|
list of tuple, tuple of int |
required |