The Mathematica Package KnotTheory`

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

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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
  • 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
  • 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 Knot Theory Software
  • KnotPlot
  • Knotscape
• Extending/Modifying KnotTheory`
• List of Modules in KnotTheory`
• How to Edit this Manual...

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