skeinIterator: Iterate the skein relation to build a skein tree of a...
In Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

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

This function is required for the computation of the skein tree of a polygonal link. The tree is built by iterating the skein relation and geometrically constructing the L_0 and L_{sw} configuration (of a Conway skein triple).

1	skeinIterator(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

`leaves`	a list containing the binary indices of the tree leaves
`tree`	a list containing the skein tree. Each slot contains the slots `points3D`, `ends`, `signs` and `M`, which are respectively the coordinates, separators of the current configuration, the skein signs of the ancestors (inner vertices) and the intersection matrix of the current configuration.

Federico Comoglio, federico.comoglio@bsse.ethz.ch

Freyd P, Yetter D, Hoste J, Lickorish WBR, Millett K, et al. (1985) A new polynomial invariant of knots and links. Bull Amer Math Soc (NS) 12: 239-246.

Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, p. 19, 1991.

Comoglio F. and Rinaldi M. A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins (2011) PLoS ONE 6(4): e18693, doi:10.1371/journal.pone.0018693 ArXiv:1104.3405

HOMFLYpolynomial,

	protein <- makeExampleProtein()
	protein <- AlexanderBriggs(protein$A)

	## Compute the skein tree
	tree <- skeinIterator(protein$points3D, protein$ends)
	str(tree)