The Alexander polynomial Δ(t) is a knot invariant computed from the Seifert matrix S: Δ(t) = det(S − t·Sᵀ). Different knots yield different polynomials — the trefoil gives 1−t+t², the figure-eight gives −1+3t−t². Explore classical knots and their invariants.
The Alexander polynomial is computed via the Seifert matrix M: Δ(t) = det(tM − MT). It is a topological invariant — unchanged by Reidemeister moves. The determinant of the knot is |Δ(−1)|.