# different results for Alexander polynomials

Hi! I just noticed that if one computes the Alexander polynomial of a knot, one gets different results according to whether the knot is presented as the closure of a braid or as a knot: t = var('t') B = BraidGroup(2) b = B([1,1,1]) knot = Knot(b) print b.alexander_polynomial() print knot.alexander_polynomial()

Output: t^-2 - t^-1 + 1 t^-1 - 1 + t Of course the polynomials differ only by a t^n multiplication, but I guess it would be better if the two coincided right away. My question is: is this issue going to be solved in the future? (I can live happily either way, just wanted to avoid modifying some stuff I'm working on!) Thanks!

Code:

and

`b.alexander_polynomial?`

gives the answer"normalized" – boolean (default: "True"); whether to return the normalized Alexander polynomial

OUTPUT:

The Alexander polynomial of the braid closure of the braid.

This is computed using the reduced Burau representation. The unnormalized Alexander polynomial is a Laurent polynomial, which is only well-defined up to multiplication by plus or minus times a power of t.

We normalize the polynomial by dividing by the largest power of t and then if the resulting constant coefficient is negative

a.s.o .