The Mathematica Package KnotTheory`

This article describes the Mathematica package KnotTheory`, the main tool used to produce The Knot Atlas.

The Jones Polynomial

• Acknowledgement
• Setup
• Naming and Enumeration
• Presentations
  • Planar Diagrams
    • Planar Diagrams: Some further details
  • Gauss Codes
  • DT (Dowker-Thistlethwaite) Codes
  • Braid Representatives
• Graphical Output
  • Drawing Planar Diagrams
    • How does DrawPD work?
  • Drawing Braids
• Structure and Operations
• Invariants
  • Invariants from Braid Theory
  • Three Dimensional Invariants
  • The Alexander-Conway Polynomial
  • The Determinant and the Signature
  • The Jones Polynomial
    • How is the Jones polynomial computed?
  • The Coloured Jones Polynomials
  • The A2 Invariant
  • The HOMFLY-PT Polynomial
  • The Kauffman Polynomial
  • Finite Type (Vassiliev) Invariants
  • 7.11 Khovanov Homology
• Extras

   * 8.1 Drawing with TubePlot
         o 8.1.1 Standalone TubePlot 

1. 9 Lightly Documented Features
2. 10 Further Knot Theory Software

   * 10.1 KnotPlot
   * 10.2 Knotscape 

1. 11 About this Manual...
2. Bibliography