Subset

class libcasm.group.Subset(

self: Subset,

group: GenericGroup,

indices: collections.abc.Set[SupportsInt | SupportsIndex] | None = None,

)

Bases: pybind11_object

Data structure specifying a subset of group elements, as indices, which may or may not form a subgroup.

Constructor

Parameters:

• group (GenericGroup) – The group this subset is part of. Must be the head group.

• indices (Optional[list[int]] = None) – Indices of the elements in the group forming the subset. If None, all elements in the group are included.

Methods

all_subgroup_generators(…)	Return a list of subgroup generators for each subgroup
all_subgroup_orbits(…)	Return a list of subgroup orbits
all_subgroups(…)	Return all subgroups of this subset
close(…)	Extend this subset to be the closure under group multiplication and return the result
cyclic_generators(…)	Return the generators of the cyclic_subgroups for this subset.
cyclic_subgroup_orbits(…)	Return a list of cyclic subgroup orbits
cyclic_subgroups(…)	Return a list of the unique cyclic subgroups (each as a Subset).
extend(…)	Extend this subset by adding indices from other and return the result.
extend_and_close(…)	Extend this subset with other then close under multiplication and return the result.
from_generators(…)	Construct a subset from subgroup generators
is_proper_subset_of(…)	Return True if this subset is a proper subset of other.
is_subset_of(…)	Return True if this subset is a subset of other (allowing equality).
left_cosets(…)	Return a list of left cosets of this subset.
maximal_cyclic_generators(…)	Return the generators of the maximal_cyclic_subgroups for this subset.
maximal_cyclic_subgroup_orbits(…)	Return a list of maximal cyclic subgroup orbits
maximal_cyclic_subgroups(…)	Return a list of maximal cyclic subgroups (each as a Subset).
minimal_generators(…)	Return a minimal set of generators for this subset.
right_cosets(…)	Return a list of right cosets of this subset.

Attributes

group	The head group this subset belongs to.
indices	The indices of elements in the head group that form this subset.
is_abelian_group	Return True if the subset is an abelian group (a commutative group where a*b == b*a for all a, b in the subset).
is_group	Return True if the subset is closed under multiplication and inverses.
is_normal	Return True if the subset is normal (invariant under conjugation).
is_simple_group	Return True if this subset is a simple group