Setup

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...

Start by downloading the file KnotTheory.zip (around 15MB), and unpack it. This will create a subdirectory KnotTheory/ in your current working directory. This done, no installation is required (though you may wish to check out Further Data Files and/or Setting the Path below). Start Mathematica and you're ready to go:

In[2]:= << KnotTheory`

Loading KnotTheory` version of March 22, 2011, 21:10:4.67737. Read more at http://katlas.org/wiki/KnotTheory.

Notice the little "prime" at the end of KnotTheory above. It is a backquote (find it on the upper left side of most keyboards) and not a quote, and it really has to be there for things to work.

Let us check that everything is working well:

In[3]:=	Alexander[Knot[6, 2]][t]
Out[3]=	-2 3 2 -3 - t + - + 3 t - t t

In[4]:= ?KnotTheoryVersion KnotTheoryVersion[] returns the date of the current version of the package KnotTheory`. KnotTheoryVersion[k] returns the kth field in KnotTheoryVersion[].

In[5]:= ?KnotTheoryVersionString KnotTheoryVersionString[] returns a string containing the date and time of the current version of the package KnotTheory`. It is generated from KnotTheoryVersion[].

In[6]:= ?KnotTheoryWelcomeMessage KnotTheoryWelcomeMessage[] returns a string containing the welcome message printed when KnotTheory` is first loaded.

Thus on the day this manual page was last changed, we had:

In[7]:=	{KnotTheoryVersion[], KnotTheoryVersionString[]}
Out[7]=	{{2011, 3, 22, 21, 10, 4.67737}, March 22, 2011, 21:10:4.67737}

In[8]:=	KnotTheoryWelcomeMessage[]
Out[8]=	Loading KnotTheory` version of March 22, 2011, 21:10:4.67737. Read more at http://katlas.org/wiki/KnotTheory.

In[9]:= ?KnotTheoryDirectory KnotTheoryDirectory[] returns the best guess KnotTheory` has for its location on the host computer. It can be reset by the user.

In[10]:=	KnotTheoryDirectory[]
Out[10]=	C:\Documents and Settings\pc\Documenti\Wolfram\KnotTheory

KnotTheoryDirectory may not work under some operating systems/environments. Please let Dror know if you encounter any difficulties.

Notes

Precomputed Data

KnotTheory` comes with a certain amount of precomputed data which is loaded "on demand" just when it is needed. When a precomputed data file is read by KnotTheory`, a notification message is displayed. To prevent these messages from appearing execute the command Off[KnotTheory::loading].

Further Data Files

To access the Hoste-Thistlethwaite enumeration of knots with 12 to 16 crossings (see Naming and Enumeration), also download either the file DTCodes4Knots12To16.tar.gz or the file DTCodes4Knots12To16.zip (about 9MB each), and unpack either one into the directory KnotTheory/.

Setting the Path

The directions above are written on the assumption that the package KnotTheory` (more precisely, the directory KnotTheory/ containing the files that make this package), is somewhere on your Mathematica search path. Usually this will be the case if KnotTheory/ is a subdirectory of your current working directory. If for some reason Mathematica cannot find KnotTheory`, you may tell it where to look in either of the following three ways. Assume KnotTheory/ is a subdirectory of FullPathToKnotTheory:

1. If you are using KnotTheory` rarely and you don't want to change system defaults, evaluate AppendTo[$Path,"FullPathToKnotTheory"] within Mathematica before attempting to load KnotTheory`.
2. If you plan to use KnotTheory` often, you may want to move the directory KnotTheory/ into one of the directories on your path. Evaluate $Path within Mathematica to see what those are.
3. Alternatively, you may permanently add FullPathToKnotTheory to your $Path. To do that, find your Mathematica base directory by evaluating $UserBaseDirectory (on Dror's laptop, this comes out to be C:\Users\Dror\AppData\Roaming\Mathematica), and then add the line AppendTo[$Path,"FullPathToKnotTheory/"] to the file $BaseDirectory/Kernel/init.m and restart Mathematica.