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

Computes the multivariable Alexander polynomial (MVA) of a polygonal link.

1 |

`points3D` |
an |

`ends` |
a vector of positive integers defining the separators of the polygonal link |

`normalized` |
logical, if FALSE (default) the multivariable non normalized MVA is returned, the normalized MVA otherwise |

`return.A` |
logical, if TRUE the Alexander matrix is returned in a format that can be parsed to sympy |

The polynomial computation relies on rSymPy. Please notice that the first time sympy is invoked is expected to be much slower than subsequent ones.

the multivariable Alexander polynomial

This is a low-level function. If you wish to make computations faster, reduce the structure first with
`AlexanderBriggs`

or `msr`

.

Maurizio Rinaldi, [email protected]

Alexander J. W. (1928) Topological invariants of knots and links. Trans. Amer. Math. Soc. 30: 275-306.

Conway J. H. (1970) An enumeration of knots and links, and some of their algebraic properties. Computational Problems in Abstract Algebra (Proc. Conf.,Oxford, 1967), Pergamon, Oxford: 329-358.

Murakami J. (1993) A state model for the multivariable Alexander polynomial. Pacific J. Math. 157, no. 1: 109-135.

Archibald J. (2008) The weight system of the multivariable Alexander polynomial. Acta Math. Vietnamica. 33: 459-470.

Archibald J. (2010) The Multivariable Alexander Polynomial on Tangles. PhD Thesis, Department of Mathematics University of Toronto

Torres G. (1953) On the Alexander polynomial Ann. Math. 57: 57-89.

Comoglio F. and Rinaldi M. (2011) A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins, PLoS ONE 6(4): e18693, doi:10.1371/journal.pone.0018693 ArXiv:1104.3405

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