Representing knots in code?

Question

So I have recently been reading some papers on the relationships of graph theory and knot theory, and that got me thinking about representing knots in code.

My current intuition on this matter is to treat the knot as essentially a planar graph, where each vertex is located at any crossing. We would then also store how the crossing was oriented for any given vertex.

Is this pretty much how it's done, or are there better ways out there?

Thanks!

Answer 1

Knots form a monad, so you can steal some representations from that world.

• http://blog.sigfpe.com/2009/05/trace-diagrams-with-monads.html
• http://blog.sigfpe.com/2008/08/untangling-with-continued-fractions.html