Graphical Input

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...

Thanks to our link with LinKnot, on Windows systems KnotTheory` accepts graphical knot input.

(For In[1] see Setup)

As in the section Using the LinKnot package, the first step is to add LinKnot to the Mathematica search path. This path will likely be different on your computer.

In[2]:=

AppendTo[$Path, "C:/bin/LinKnot/"];

In[3]:= ?KnotInput KnotInput[] opens a window in which you can draw a knot or link by hand. Right click and select 'Quit' when you're done. This function requires the package LinKnots`, and will only run on Windows machines. Sorry!

In[4]:= KnotInput::about The KnotInput program was written by M. Ochiai, C. Nakai, Y. Matsuyama and N. Imafuji and is imported to KnotTheory` via the package LinKnot by S. Jablan and R. Sazdanovic

Thus for example, the input line

In[5]:=

K = KnotInput[]

pops a blank window on which a knot or a link can be drawn with mouse clicks. At first pass all crossings are drawn as "new over old", but a further click on any given crossing will flip it.

KnotInput in action.

A right click followed by selecting "quit" will then determine the Gauss code of the knot or link just drawn and return it to Mathematica:

Out[5]=

GaussCode[{-1,-4,2,3},{-3,-5,4,6},{5,1,-6,-2}]

K is now perfectly usable within KnotTheory`:

In[5]:=	$K=GaussCode[{-1,-4,2,3},{-3,-5,4,6},{5,1,-6,-2}];$
Out[5]=	$

In[6]:=	Kh[K][q, t]
Out[6]=	1 - + q q