orientations#

orientations(k, up_to_reversal=False)#

Generate all orientations of an unoriented diagram.

If up_to_reversal is True, the first edge is always oriented “forward” and only the remaining edges are flipped (removing a global reversal).

Parameters:

  • k (PlanarDiagram) – Unoriented diagram.

  • up_to_reversal (bool) – If True, return orientations modulo global reversal.

Returns:

List of OrientedPlanarDiagram.

Return type:

list[OrientedPlanarDiagram]

Notes

  • If k is already oriented, it is first “unoriented” (structure preserved) and then all orientations are generated.

  • If k.name is set, each result’s name is suffixed with a string of “+”/“–” per-edge choices (useful for debugging).

Example

>>> import knotpy as kp
>>> k = kp.knot("3_1")
>>> k1, k2 = kp.orientations(k)
>>> print(f'Oriented trefoils: {k1} and {k2}')
Oriented diagrams: Diagram named 3_1+ a → X(b3o c0i c3i b0o), b → X(a3i c2o c1o a0i), c → X(a1o b2i b1i a2o) and Diagram named 3_1- a → X(b3i c0o c3o b0i), b → X(a3o c2i c1i a0o), c → X(a1i b2o b1o a2i)
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