join#
Join diagrams by a bridge or by introducing a crossing.
Functions
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Join two diagrams by inserting a length-1 bridge (a degree-3 vertex on each side, linked together). |
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Join two diagrams by a cut crossing (twisted connected sum). |
- bridge_join(a, b, arcs)#
Join two diagrams by inserting a length-1 bridge (a degree-3 vertex on each side, linked together).
- Parameters:
a (PlanarDiagram | OrientedPlanarDiagram) – Two diagrams of the same type.
b (PlanarDiagram | OrientedPlanarDiagram) – Two diagrams of the same type.
arcs (Tuple[frozenset[Endpoint], frozenset[Endpoint]] | None) – A pair of arcs (one from a, one from b) as frozensets of two endpoints. If None, the first available arc from each diagram is used.
- Returns:
A new diagram of the same type that is the bridged join of a and b.
- Raises:
TypeError – If a and b are not of the same diagram type.
- Return type:
- crossing_join(a, b, arcs)#
Join two diagrams by a cut crossing (twisted connected sum).
- Parameters:
a (PlanarDiagram | OrientedPlanarDiagram) – Two diagrams of the same type.
b (PlanarDiagram | OrientedPlanarDiagram) – Two diagrams of the same type.
arcs (Tuple[frozenset[Endpoint], frozenset[Endpoint]] | None) – A pair of arcs (one from a, one from b) as frozensets of two endpoints. If None, the first available arc from each diagram is used.
- Returns:
A new diagram with a new crossing that joins the two inputs along the chosen arcs.
- Raises:
TypeError – If a and b are not of the same diagram type.
- Return type: