I'm trying to detect the crossing number (or another knot invariant) of a simulated polymer. A polymer is a closed bead spring, which means that it is represented by a set of points connected by segments which form a closed curve. I need to extract from this set of points a number which would let me classify the knots of the polymer.
I was doing some research and I found the self-linking number which would be the linking number between the curve and a framing of it, but I don't expect a good numerical stability from this algorithm although I am maybe wrong.
Actually, at this point, I would be satisfied just to find a numerical operator which would let me discern trefoil-knot from no-knot since I doubt that I have other kind of knots.
As an example, here are two polymer configurations which should both be trefoil knots: