Gauss Codes

The Gauss Code of an $n$-crossing knot or link $L$ is obtained as follows:

• Number the crossings of $ L$ from 1 to $ n$ in an arbitrary manner.
• Order the components of $ L$ is some arbitrary manner.
• Start ``walking along the first component of $ L$, taking note of the numbers of the crossings you've gone through. If in a given crossing crossing you cross on the ``over strand, write down the number of that crossing. If you cross on the ``under strand, write down the negative of the number of that crossing.
• Do the same for all other components of $ L$ (if any).

The resulting list of signed integers (in the case of a knot) or list of lists of signed integers (in the case of a link) is called the Gauss Code of $L$. KnotTheory` has some rudimentary support for Gauss codes: