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

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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)

Rknots documentation built on May 29, 2017, 1:38 p.m.

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