## Obtaining the other Alexander Polynomials

Once the Alexander-Conway polynomial has been obtained, one may proceed
straight forwardly to find the other determinants that are relevant. To obtain
the *Greatest Common Divisor* one should notice that possible factors
are of the form

*a t^{2k} + b t^{2k-1} + c t^{2k-2} + ... +q t^k + ... + c t^2 + b t + a
*

where 2(a+b+c+...)+q = \pm 1, and k.LE.n, where 2n is the power of
the Alexander-Conway polynomial.
In addition, *a* is a divisor of the constant term of the
polynomial one wants to factorise. Therefore the possibilities are limited and
by exhausting them one may find if there are non-trivial Alexander polynomials
besides the Alexander-Conway, and their respective values. As a rule, most
knots do not have non-trivial such polynomials.
To proceed with explicit results, click
**here**.

*Charilaos Aneziris, aneziris@hades.ifh.de*

**Copyright 1995**

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