There are three packages here,
- Braids.m which draws various pictures of plats and open and closed braids. It
uses the other two. It is the heart of the matter and is meant as a basis for
doing differential geometry with framed knots and links.
- BraidGroup.m which does algebra in Artin's braid group.
and
- SymmetricGroup.m which does algebra in the symmetric group.
There is also a notebook,
- WhizzoKeenBraids.ma which contains various examples of aesthetically and
mathematically interesting braids.
Braids are represented in the form {cs, s}, where cs is a list of crossings
and s is the number of strands. Individual crossings are represented by
integers: -n when the nth strand crosses under the n+1st, n when the nth
strand crosses over the n+1st."