I have to implement a knot algorithm, which is given in a quite abstract form. It sounds like "follow the line to iterate over all tangles".
How can tangles be represented in a computer? In other words, given a kind of knot representation in computer memory (which one lies within the reader's choice), how can I get a machine representation of its tangles? (Note: Tangles and crossings are different things.)
It may sound that this question is more appropriate for StackOverflow, but I doubt that the community there has enough knowledge of knot theory.
The program SnapPy has a built in module that lets you construct knots out of tangles. This is sometimes quite simple depending on the type of knots or links you are interested in and sometimes very challenging. But it should basically always be possible. Once your knot is built, you then have all of SnapPy at your disposal to compute invariants of it.
There are instructions on that site that tell you how it works. Good luck.