So I happen to like proteins quite a lot and one thing that is very similar to a protein, when represented as the bare minimum, is a 1D curve embedded in the 3D space. They form beautiful and unique shapes and the particular way in which the curve winds itself matters a lot to the chemistry of proteins in general, which is a HUGE deal for every living system we know of.
So in my burning passion for proteins and math I have done a lot of things to those curves, and one thing I'd like to do now is play with Knot Theory.
What I have in my hands is a collection of points in order (the curve). Usually these polymers are linear, meaning that they have two ends, like a rope, but I can assume they are cyclic and that they fuse together at the ends just for purposes of calculating knot invariants, as if the protein itself was one huge knot. I'm not awfully proficient in Knot Theory, but I'd like to look for patterns in these invariants for my protein database.
What I would like to know is:
Is there a software out there which would help me calculate knot invariants for these curves in 3D space (given that their ends are fused together)?