Template:Rolfsen Knot Presentations Computer Talk

The session shown below is meant to be similar to the notebook in http://katlas.org/svn/KnotAtlas/RolfsenKnotPageSession.nb

Computer Talk[hide]

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091. Read more at http://katlas.org/wiki/KnotTheory.

In[3]:=

K = Knot["Rolfsen Knot Presentations Computer Talk"];

In[4]:=

PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

Data:Rolfsen Knot Presentations Computer Talk/PD Presentation

In[5]:=

GaussCode[K]

Out[5]=

1, -4, 3, -6, 5, -1, 2, -3, 6, -8, 7, -5, 4, -2, 8, -7

In[6]:=

DTCode[K]

Out[6]=

Data:Rolfsen Knot Presentations Computer Talk/DT Code

(The path below may be different on your system)

In[7]:=

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

In[8]:=

ConwayNotation[K]

Out[8]=

Data:Rolfsen Knot Presentations Computer Talk/Conway Notation

In[9]:=

br = BR[K]

KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.

Out[9]=

Data:Rolfsen Knot Presentations Computer Talk/BraidWord

In[10]:=

{First[br], Crossings[br], BraidIndex[K]}

KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.

KnotTheory::loading: Loading precomputed data in IndianaData`.

Out[10]=

{ Data:Rolfsen Knot Presentations Computer Talk/MinimalBraidWidth, Data:Rolfsen Knot Presentations Computer Talk/MinimalBraidLength, Data:Rolfsen Knot Presentations Computer Talk/BraidIndex }

In[11]:=

Show[BraidPlot[br]]

Data:Rolfsen Knot Presentations Computer Talk/BraidPlot

Out[11]=

-Graphics-

In[12]:=

Show[DrawMorseLink[K]]

KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."

KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."

File:Rolfsen Knot Presentations Computer Talk ML.gif

Out[12]=

-Graphics-

In[13]:=

ap = ArcPresentation[K]

Out[13]=

ArcPresentation[{7, 10}, {9, 2}, {10, 4}, {3, 5}, {4, 8}, {6, 9}, {5, 1}, {2, 7}, {1, 6}, {8, 3}]

In[14]:=

Draw[ap]

File:Rolfsen Knot Presentations Computer Talk AP.gif

Out[14]=

-Graphics-