The Mathematica Package KnotTheory`

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

• Acknowledgement
• Setup
• Naming and Enumeration
• Presentations
  • Planar Diagrams
    • Some further details
  • Gauss Codes
  • DT (Dowker-Thistlethwaite) Codes
  • Braid Representatives
• Graphical Output
  • Drawing Planar Diagrams
    • Drawing Planar Diagrams#How does it 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
    • 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 Included with KnotTheory`
  • Drawing with TubePlot
    • Drawing with TubePlot#Standalone TubePlot
  • WikiLink - The Mediawiki Interface
  • WikiLink - The Mediawiki Interface#Standalone WikiLink
• Lightly Documented Features
• Further Knot Theory Software
  • Further Knot Theory Software#KnotPlot
  • Further Knot Theory Software#Knotscape
• About this Manual...
• Bibliography