Rknots (version 1.3.2)

computeInvariant: Compute an invariant of an object of class 'Knot'

Description

Compute one polynomial invariant (HOMFLY, Jones, Alexander, multivariable Alexander) of a knot or link, or the linking number of a link for object of class 'Knot'.

Usage

computeInvariant(knot, invariant, ...)

Arguments

knot

an object of class 'Knot'

invariant

'HOMFLY' for the HOMFLY polynomial, 'Alexander' for the Alexander polynomial (knots) or the multivariable Alexander polynomial (links), 'Jones' for the Jones polynomial, 'LK' for the linking number of a link

...

additional parameters to be passed to lower level functions (e.g. skein.sign for the HOMFLY polynomial computation

Value

the computed invariant

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. (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 Alexander J. W. (1928) Topological invariants of knots and links. Trans. Amer. Math. Soc. 30: 275-306. Conway J. H. (1970) An enumeration of knots and links, and some of their algebraic properties. Computational Problems in Abstract Algebra (Proc. Conf.,Oxford, 1967), Pergamon, Oxford: 329-358.

Murakami J. (1993) A state model for the multivariable Alexander polynomial. Pacific J. Math. 157, no. 1: 109-135.

Archibald J, (2008) The weight system of the multivariable Alexander polynomial. Acta Math. Vietnamica. 33: 459-470. Archibald J. (2010) The Multivariable Alexander Polynomial on Tangles. PhD Thesis,Department of Mathematics University of Toronto

Torres G. (1953) On the Alexander polynomial Ann. Math. 57: 57-89.

See Also

Knot-class

Examples

## Not run: 
# knot <- makeExampleKnot(k = TRUE)
# knot <- newKnot(knot)
# 
# ##compute the polynomials
# computeInvariant(knot, 'HOMFLY', skein.sign = -1)
# computeInvariant(knot, 'Alexander')
# ## End(Not run)