# Alexander polynomials for Pretzel knots

All knots, such as this torus knot,

KnotData[{"TorusKnot", {3, 5}}]


have an associated Alexander polynomial:

KnotData[{"TorusKnot", {3, 5}}, "AlexanderPolynomial"][x]


$$x^4+\frac{1}{x^4}-x^3-\frac{1}{x^3}+x+\frac{1}{x}-1 .$$

Why aren't the Alexander polynomials for a pretzel knot, such as this,

available?

KnotData[{"PretzelKnot", {5, 4, 3}}, "AlexanderPolynomial"]

Missing["NotAvailable"]

• I guess that the properties in KnotData are not computed on the fly but that they are tabulated. I am not sure; maybe the "KnotTheory" package can help you further. Dec 15, 2018 at 7:14
• Supporting Henrik's supposition, comparing Length@KnotData[{"PretzelKnot", {5, 4, 3}}, "Properties"] (i.e., 67) with Length@DeleteCases[KnotData[{"PretzelKnot", {5, 4, 3}}, #]& /@ KnotData[{"PretzelKnot", {5, 4, 3}}, "Properties"], Missing["NotAvailable"]] (i.e., 15`), you see that most of the knot properties are not available for this particular knot. Dec 15, 2018 at 15:37