The braid programme was originally written to calculate matrix representations of virtual braid groups. It has evolved to include tasks that relate to virtual knots, long knots, welded knots and knotoids but that do not involve a braid representation. However, in the absence of anything better, the name 'braid' has been retained for the programme.
The tools provided by the programme support the following:
Alexander and Burau polynomial invariant
Alexander-like polynomial invariant of a classical doodle
Burau, or generalized Alexander, polynomial invariant
Commutative automorphism switch invariants
Finite-switch polynomial invariants (also known as rack polynomials)
Fixed-point invariant of the braid representation of a knot or doodle
Colouring number invariant for virtual knots, links or doodles
Cocycle state sum invariants including the doubled-birack cocycle invariant
Birack polynomial invariants based on colouring numbers or cocycles
Matrix-switch polynomial invariants
Quaternionic polynomial invariants
Sawollek's normalized Conway polynomial for a braid word
Weyl algebra switch polynomial invariants
Arrow polynomial of a classical or virtual knot, link, long knot, long virtual knot, knotoid or multi-knotoid
HOMFLY polynomial
Jones polynomial of a classical or virtual knot, link, knotoid or multi-knotoid
Kauffman's Affine Index Polynomial for virtual knots or knotoids
Kauffman bracket polynomial of a classical or virtual knot, link, knotoid or multi-knotoid
Manturov-Nikonov Alexander-like polynomial for flat virtual knots
Turaev's extended bracket polynomial of a classical or virtual knotoid or multi-knotoid
Parity arrow polynomial of a classical or virtual knot or knotoid
Parity bracket polynomial of a classical or virtual knot or knotoid
Dynnikov test for the trivial braid
Hamiltonian circuits within classical or flat knot or link diagram
Vogel's algorithm for determining a braid word from a knot or link diagram
The turning number of a knot or link diagram
Prime test to determine whether the shadow of a classical or virtual knot, link, knotoid or multi-linkoid diagram is 3-connected
The strand permutation determined by a braid
Homology and cohomology generator evaluation for biracks
Dowker(-Thistlethwaite) code for a braid or labelled peer code
Gauss code for a labelled peer code or the closure of a braid word
Labelled immersion code for a braid word
Labelled peer code for
braid word of a classical or virtual knot or link
labelled immersion code of a classical or virtual knot or link
Gauss code of a classical, virtual or flat link, knotoid, multi-knotoid or multi-linkoid
Labelled peer code for the planar diagram description (PD code) of a classical or virtual link
the n-parallel cable satellite of a knot's peer code