linkingNumber: Compute the linking number of a polygonal link
In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Compute the linking number of a polygonal link

1	linkingNumber(points3D, ends, M = c())

`points3D`	an N x 3 matrix of the x, y, z coordinates of a polygonal link
`ends`	a vector of positive integers defining the separators of the polygonal link
`M`	the intersection matrix of the polygonal link. If no matrix is provided, the function will compute it (default)

The linking number is defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components α and β,

lk(α, β) = \frac{1}{2} ∑_{c \in α \cap β} ε(c)

where α \cap β is the set of crossings of α with β, and ε(c) is the sign of the crossing.