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  • The PD notation used by KnotTheory` is inadequate when a knot diagram contains kinks. For example, there is no way to tell the orientation of PD[X[1,1,2,2]]. You can define braids with kinks, though: Kink = BR[2, {1}]. All knot invariants defined for braid representatives will be correctly evaluated. For example, the previously defined Kink will of course have the same invariants as the unknot. However, don't try to transform the braid into a planar diagram (PD[BR[2, {1}]]), as mathematica might hang up on that.
  • Many knot invariants (including Jones) do not understand the (artificial but necessary) PD construct "Loop".
  • Mathematica 9 defines its own tensor product, which causes bugs with the QuantumGroups` package. Stick with Mathematica 7 or 8 until Scott has it fixed.
  • For some unexplicable bugs (in Mathematica 8 only?), it appears helpful to state the "context" explicitly, e.g. KnotTheory`BR instead of BR, or MirrorTrefoil = PD[KnotTheory`X[1, 5, 2, 4], KnotTheory`X[3, 1, 4, 6], KnotTheory`X[5, 3, 6, 2]] instead of MirrorTrefoil = PD[X[1, 5, 2, 4], X[3, 1, 4, 6], X[5, 3, 6, 2]].