polyConversion: Convert the HOMFLY polynomial into the Alexander or Jones...

In FedericoComoglio/Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

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

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}

Value

The Alexander or the Jones polynomial

Note

These are low-level functions.

Author(s)

Federico Comoglio, [e-mail]

Maurizio Rinaldi, [e-mail]

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

## Not run: 
HOMFLY.trefoil <- "-1/l**4 + 2/l**2 + m**2/l**2"
HOMFLY2Alexander(HOMFLY.trefoil)
HOMFLY2Jones(HOMFLY.trefoil)

## End(Not run)

FedericoComoglio/Rknots documentation built on May 6, 2019, 4:35 p.m.