Rknots (version 1.3.0)

HOMFLY2Jones: Convert the HOMFLY polynomial into the Alexander or Jones polynomials

Description

Convert the HOMFLY polynomial into the Alexander or Jones polynomials

Usage

HOMFLY2Alexander(HOMFLY)
HOMFLY2Jones(HOMFLY)

Arguments

HOMFLY

a single element character vector containing the HOMFLY polynomial

Value

• The Alexander or the Jones polynomial

Details

The Alexander polynomial is obtained by substituting into the HOMFLY polynomial $$l=1$$ and $$m=x^{1/2} - x^{-1/2}$$ The following substitutions lead instead to the Jones polynomial $$l=t^{-1}$$ and $$m=t^{1/2} - t^{-1/2}$$

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.

See Also

HOMFLYpolynomial

Examples

HOMFLY.trefoil <- "-1/l**4 + 2/l**2 + m**2/l**2"
HOMFLY2Alexander(HOMFLY.trefoil)
HOMFLY2Jones(HOMFLY.trefoil)