skeinIterator: Iterate the skein relation to build a skein tree of a polygonal link
Description
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).
Usage
skeinIterator(points3D, ends, M = c())
Arguments
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
Value
References
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
protein <- makeExampleProtein()
protein <- AlexanderBriggs(protein$A)
## Compute the skein tree tree <- skeinIterator(protein$points3D, protein$ends)
str(tree)