Convert the HOMFLY polynomial into the Alexander or Jones polynomials

Description

Convert the HOMFLY polynomial into the Alexander or Jones polynomials

Usage

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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, federico.comoglio@bsse.ethz.ch

Maurizio Rinaldi, maurizio.rinaldi@pharm.unipmn.it

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

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

## End(Not run)

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