I need to discretise Gauss's linking number formula, to be used for finding the the linking number of a given topological conformation of say a ring like polymer chain (mainly Hopf link) . The discretisation is needed since the chain consists of beads/monomers connected via spring. As a result the distance between consecutive monomers can change.
Generally, when we discretise, the measure "dr" consists of a segment of the ring, but since here the ring can itself change in shape, i couldn't understand how to apply the Gauss's linking number formula?
Is it better to use Alexander polynomial to find the linking number in these cases?