I am looking for a bit of orientation with regards to computational topology resources, as I am personally totally ignorant on the subject. I have lots of different links in $S^3$ (hundreds of millions) lying around in some boxes my garage and I would like to start sorting through them and getting rid of the ones that are not unlinks. What software should I load these links into to do this (efficiently)?


I know there are some invariants I can compute that will detect unlinks but this is probably a bit computationally expensive to compute on every link. For example, it will probably cut down on the computation a lot if I first just compute some pairwise linking numbers of the components and throw out any links where these do not vanish. After doing that maybe I should check that the individual components at least seem to be unknotted (maybe by computing the Alexander polynomial?). What sorts of invariants would you compute to try and sort through the whole garage in a reasonable amount of time?



Looking through a bunch of links for unlinks?
It will of course depend on where your examples are coming from. But here are some lightweight approaches.


1. Randomize the triangulation of the link complement a few times and then simplify. Do you get a standard triangulation of the unlink complement? (Regina and Snappy will both do something like this.)
2. Compute the Alexander polynomial. (Snappy running under sage will do this.)
3. Compute a presentation of the fundamental group. (Regina and Snappy will both do this.)
4. Think about using hyperbolic geometry or normal surface theory. But these will be slower...


