connected_sum#
” Two knots (or links or planar diagrams) can be summed by placing them side by side and joining them by straight bars so that orientation is preserved in the sum. The knot sum is also known as composition (Adams 1994) or connected sum (Rolfsen 1976, p. 40).
- is_connected_sum(k)#
Determine if the given planar diagram represents a connected sum.
A connected sum is checked if there is an arc-cut-set of order 2, i.e. removing two arcs from the diagram disconnects it into two components.
- Parameters:
k (PlanarDiagram | OrientedPlanarDiagram) – A planar diagram to check for connected sum property.
- Returns:
bool – True if the diagram is a connected sum; otherwise, False.
- Return type:
bool
- is_connected_sum_third_order(g)#
Return True if g is a 3rd order connected sum diagram and False otherwise.
- Parameters:
g (PlanarDiagram)
- Return type:
bool
- connected_sum_decomposition(k)#
Return a list of connected sum components.
- Parameters:
k (PlanarDiagram)
- Return type:
list
- connected_sum(a, b, arcs=None)#
- Parameters:
arcs (None | list | tuple)
- Return type: