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"]
KnotDataare not computed on the fly but that they are tabulated. I am not sure; maybe the"KnotTheory`"package can help you further. $\endgroup$Length@KnotData[{"PretzelKnot", {5, 4, 3}}, "Properties"](i.e.,67) withLength@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. $\endgroup$