httk.atomistic.symmetry.subgroups¶

Graph queries and exact transformations for Bärnighausen subgroup trees.

The vendored tables contain maximal subgroup relations and their standard-setting transformations for all 230 space-group types. Only those one-hop relations are tabulated; closures and the inverted supergroup graph are derived here.

The split-affine convention pinned by tests/test_subgroups.py is that a WyckoffSplitPiece operation maps a parent standard-setting coordinate directly to a child standard-setting coordinate. The tabulated SubgroupTransform operation has matrix M with the child basis on the left: B_child = M.T() * B_parent. At the affine-coordinate level it maps child coordinates into parent coordinates, f_parent = f_child * M.T() + v; its inverse matrix is the coordinate basis change used by the split operations (up to their listed origin translations).

Classes¶

`SubgroupRepresentationResult`	Store an exact asymmetric-unit representation in a subgroup.
`WyckoffSplitPiece`	One child Wyckoff piece in a maximal subgroup transformation.
`SubgroupTransform`	One exact standard-setting transformation in a maximal subgroup table entry.

Functions¶

`maximal_subgroups`(spacegroup)	Return the distinct tabulated maximal-subgroup IT numbers.
`minimal_supergroups`(spacegroup)	Return the distinct tabulated minimal-supergroup IT numbers.
`subgroup_closure`(spacegroup, *[, include_self])	Return the graph-derived transitive subgroup closure.
`supergroup_closure`(spacegroup, *[, include_self])	Return the graph-derived transitive supergroup closure.
`subgroup_transforms`(parent, subgroup)	Return every tabulated transform for one parent/target pair.

Module Contents¶

class httk.atomistic.symmetry.subgroups.SubgroupRepresentationResult[source]¶

Store an exact asymmetric-unit representation in a subgroup.

Parameters:

asu – The subgroup-standard-setting asymmetric unit with identity transform.
spacegroup – The subgroup space group in its standard setting.
path – The selected maximal-subgroup transforms, in parent-first order.
multiplier – The exact child-to-parent cell-content ratio.

asu: httk.atomistic.models.structure.asu.ASUStructure[source]¶

spacegroup: httk.atomistic.symmetry.spacegroup.Spacegroup[source]¶

path: tuple[SubgroupTransform, Ellipsis][source]¶

multiplier: fractions.Fraction[source]¶

class httk.atomistic.symmetry.subgroups.WyckoffSplitPiece[source]¶

One child Wyckoff piece in a maximal subgroup transformation.

Parameters:

letter – The child-setting Wyckoff letter as tabulated.
xyz – The tabulated coordinate expression, for display and provenance.
operation – The exact affine map from a parent standard-setting coordinate directly to a child standard-setting coordinate.

letter: str[source]¶

xyz: str[source]¶

operation: httk.atomistic.symmetry.affine_operation.AffineOperation[source]¶

class httk.atomistic.symmetry.subgroups.SubgroupTransform[source]¶

One exact standard-setting transformation in a maximal subgroup table entry.

Parameters:

parent – The parent space group in its IT standard setting.
subgroup – The subgroup in its IT standard setting.
index – The tabulated subgroup index [G:H].
subgroup_type – The tabulated relation type, "t" or "k".
k_subtype – The tabulated k subtype, or None for a t relation.
operation – The exact tabulated affine basis change from child to parent coordinates. If its matrix is M and vector is v, it evaluates as f_parent = f_child * M.T() + v; the child basis is M.T() * parent_basis.
splittings – An immutable mapping from parent Wyckoff letters to child pieces.

parent: httk.atomistic.symmetry.spacegroup.Spacegroup[source]¶

subgroup: httk.atomistic.symmetry.spacegroup.Spacegroup[source]¶

index: int[source]¶

subgroup_type: str[source]¶

k_subtype: str | None[source]¶

operation: httk.atomistic.symmetry.affine_operation.AffineOperation[source]¶

splittings: collections.abc.Mapping[str, tuple[WyckoffSplitPiece, Ellipsis]][source]¶

httk.atomistic.symmetry.subgroups.maximal_subgroups(spacegroup)[source]¶

Return the distinct tabulated maximal-subgroup IT numbers.

Self-referencing isomorphic entries are excluded from graph navigation.

Parameters:: spacegroup (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – A space group or IT number identifying the parent.
Returns:: Sorted unique target IT numbers, excluding spacegroup itself.
Raises:: KeyError – If the IT number has no vendored subgroup record.
Return type:: tuple[int, Ellipsis]

httk.atomistic.symmetry.subgroups.minimal_supergroups(spacegroup)[source]¶

Return the distinct tabulated minimal-supergroup IT numbers.

Self-referencing isomorphic entries are excluded from graph navigation.

Parameters:: spacegroup (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – A space group or IT number identifying the subgroup.
Returns:: Sorted unique parent IT numbers, excluding spacegroup itself.
Raises:: KeyError – If the IT number has no vendored subgroup record.
Return type:: tuple[int, Ellipsis]

httk.atomistic.symmetry.subgroups.subgroup_closure(spacegroup, *, include_self=False)[source]¶

Return the graph-derived transitive subgroup closure.

Parameters:

spacegroup (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – A space group or IT number identifying the parent.
include_self (bool) – Include the root IT number in the result.

Returns:

Sorted reachable subgroup IT numbers.

Raises:

KeyError – If the IT number has no vendored subgroup record.

Return type:

tuple[int, Ellipsis]

httk.atomistic.symmetry.subgroups.supergroup_closure(spacegroup, *, include_self=False)[source]¶

Return the graph-derived transitive supergroup closure.

Parameters:

spacegroup (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – A space group or IT number identifying the subgroup.
include_self (bool) – Include the root IT number in the result.

Returns:

Sorted reachable supergroup IT numbers.

Raises:

KeyError – If the IT number has no vendored subgroup record.

Return type:

tuple[int, Ellipsis]

httk.atomistic.symmetry.subgroups.subgroup_transforms(parent, subgroup)[source]¶

Return every tabulated transform for one parent/target pair.

Results retain table order, including self-targeted isomorphic entries. The returned tuple is empty when the pair has no tabulated relation.

Parameters:

parent (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – The parent space group or IT number.
subgroup (httk.atomistic.symmetry.spacegroup.Spacegroup | int) – The subgroup space group or IT number.

Returns:

All exact standard-setting transformations for the pair.

Raises:

KeyError – If either IT number has no vendored subgroup record.

Return type:

tuple[SubgroupTransform, Ellipsis]