Bugs

KnotTheory`/Navigation  The Mathematica Package KnotTheory` Acknowledgement Setup Naming and Enumeration Presentations Planar Diagrams Some further details Gauss Codes DT (Dowker-Thistlethwaite) Codes Braid Representatives MorseLink Presentations Arc Presentations Conway Notation Graphical Input Graphical Output Drawing Planar Diagrams How does it work? Drawing MorseLink Presentations Drawing Braids Structure and Operations Invariants Invariants from Braid Theory Three Dimensional Invariants The Alexander-Conway Polynomial The Multivariable Alexander Polynomial The Determinant and the Signature The Jones Polynomial How is the Jones polynomial computed? The Coloured Jones Polynomials The A2 Invariant Quantum knot invariants The HOMFLY-PT Polynomial The Kauffman Polynomial Finite Type (Vassiliev) Invariants Khovanov Homology Heegaard Floer Knot Homology R-Matrix Invariants Extras Included with KnotTheory` Drawing with TubePlot Standalone_TubePlot Using the LinKnot package WikiLink QuantumGroups` Lightly Documented Features A Sample KnotTheory` Session Further Usage Example Prime Links with a Non-Prime Component "Rubberband" Brunnian Links Identifying Knots within a List Cabling Burau's Theorem Further Knot Theory Software KnotPlot Knotscape Xknots Extending/Modifying KnotTheory` Bugs How to Edit this Manual...

• 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]].