# Convert the HOMFLY polynomial into the Alexander or Jones polynomials

### Description

Convert the HOMFLY polynomial into the Alexander or Jones polynomials

### Usage

1 2 | ```
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, 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

1 2 3 4 5 6 | ```
## 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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