In this note we give concise formulas, which lead to a simple and
fast computer program that computes a powerful knot invariant. This
invariant $\rho_1$ is not new, yet our formulas are by far the simplest
and fastest: given a knot we write one of the standard matrices $A$
whose determinant is its Alexander polynomial, yet instead of
computing the determinant we consider a certain quadratic expression in
the entries of $A^{-1}$. The proximity of our formulas to the Alexander
polynomial suggest that they should have a topological explanation. This
we don't have yet. Yet we do know that $\rho_1$ yields a lower bound on
the genus of a knot, and that it is sometimes better than the lower
bound coming from the Alexander polynomial.
