HOMFLYpolynomial: Compute the HOMFLY polynomial 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 HOMFLY polynomial of a polygonal link, given its skein tree (generated by skeinIterator)

1	HOMFLYpolynomial(leaves, tree, skein.sign = -1)

`leaves`	a list containing the binary indices of the tree leaves
`tree`	a list containing the skein tree as returned by `skeinIterator`.
`skein.sign`	the skein sign to be used (+1 or -1)

The polynomial computation relies on rSymPy. Please notice that the first time sympy is invoked is expected to be much slower than subsequent ones.

the HOMFLY polynomial

This is a low-level function.

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

HOMFLY2mirror, HOMFLY2Alexander, HOMFLY2Jones

## Not run: 
## Import a PDB file from the file system
protein <- makeExampleProtein()

## Reduce to minimal structure
protein.reduced <- AlexanderBriggs(protein$A)

## Compute the skein tree
tree <- skeinIterator(protein.reduced$points3D, protein.reduced$ends)
	
## Compute the HOMFLY polynomial
HOMFLYpolynomial(tree$leaves, tree$tree, skein.sign = -1)

## End(Not run)