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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