Lightly Documented Features

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...

(For In[1] see Setup)

In[1]:= ?NumberOfKnots NumberOfKnots[type] return the number of knots of a given type.

In[2]:=	NumberOfKnots[16, NonAlternating]
Out[2]=	1008906

In[3]:= ?MorseLink MorseLink[K] returns a presentation of the oriented link K, composed, in successive order, of the following 'events': Cup[m,n] is a directed creation, starting at strand position n, towards position m, where m and n differ by 1. X[n,a = {Over/Under}, b = {Up/Down}, c={Up/Down}] is a crossing with lower-left edge at strand n, a determines whether the strand running bottom-left to top-right is over/under the crossing, b and c give the directions of the bottom-left and bottom-right strands respectively through the crossing. Cap[m,n] is a directed cap, from strand m to strand n.

In[4]:= MorseLink::about MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005.

In[5]:=	MorseLink[Knot[3, 1]]
Out[5]=	MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up], X[2, Under, Up, Up], 2 ? 1, 1 ? 2]

In[6]:= ?DrawMorseLink DrawMorseLink[L] returns a drawing of the knot or link L as a "Morse Link". For diagrams with a large number of crossings, it may be helpful to use one or both of the options as in DrawMorseLink[L, Gap -> g, ArrowSize -> as ], with 0 < as, g < 1, where g controls the amount of white space at each crossing, and as controls the size of the orientation arrows.

In[7]:= DrawMorseLink::about DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.

In[9]:=	Show[DrawMorseLink[Link[11, Alternating, 548]]]
Out[9]=	-Graphics-