SymGroup#

class libcasm.sym_info.SymGroup( self: SymGroup, elements: collections.abc.Sequence[SymOp], multiplication_table: collections.abc.Sequence[collections.abc.Sequence[SupportsInt]], )#

Bases: pybind11_object

Data structure holding group elements and other group info, such as group-subgroup relationships.

The SymGroup class goes beyond storing a list[SymOp] to include the multiplication table and inverse element table. The SymGroup class may represent a head group, or a subgroup.

When representing a subgroup, the head group can be obtained as a shared pointer from head_group(). Pointers to subgroups are not stored by the head group. For subgroups, there is a list of indices indicating which element in the head group each subgroup element corresponds to (head_group_index()).

The libcasm.sym_info package provides factory functions for the common use cases of constructing the prim factor group and prim point group:

Factory Functions

make_factor_group(): Make the libcasm.xtal.Prim factor group
make_point_group(): Make the libcasm.xtal.Prim point group

Special methods

Get the i-th element of the group using: element = group[i]

Constructor

Parameters:

elements (list[SymOp]) – The matrix representation of elements of the group.
multiplication_table (list[list[int]]) – The multiplication table element multiplication_table[i][j] == k represents that np.allclose(elements[k], elements[i] @ elements[j]) == True.

Methods

`brief_cart`(…)	Brief description, in Cartesian coordinates
`brief_frac`(…)	Brief description, in fractional coordinates
`conjugacy_classes`(…)	Returns the conjugacy classes
`from_dict`(…)	Construct a SymGroup from a Python dict.
`from_elements`(…)
`inv`(…)	Returns the index of the inverse of an element
`make_subgroup`(…)	Make a subgroup
`mult`(…)	Returns the index of the element product.
`to_dict`(…)	Represent the SymGroup as a Python dict

Attributes

`elements`	The elements list
`head_group`	The head group if this is a subgroup, else None.
`head_group_index`	The list of head group indices (guaranteed sorted)
`inverse_index`	The list of inverse indices
`is_subgroup`	True if this is a subgroup, False otherwise.
`multiplication_table`	The multiplication table.