Rknots (version 1.3.0)

HOMFLY2mirror: Convert the HOMFLY polynomial of a knot into the polynomial of its mirror image

Description

The HOMFLY polynomial of the mirror image of a knot is computed by substituting $$l=-l^{-}1$$

Usage

HOMFLY2mirror(HOMFLY)

Arguments

HOMFLY

a single element character vector containing the HOMFLY polynomial

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, HOMFLY2Alexander, HOMFLY2Jones

Examples

##convert the right-handed trefoil knot polynomial into the left-handed trefoil polynomial
HOMFLY.trefoil <- "-1/l**4 + 2/l**2 + m**2/l**2"
HOMFLY2mirror(HOMFLY.trefoil)