Template:Rolfsen Knot Presentations Computer Talk: Difference between revisions

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<noinclude>The session shown below is meant to be similar to the notebook in http://katlas.org/svn/KnotAtlas/RolfsenKnotPageSession.nb</noinclude>
<div class="NavFrame"><div class="NavHead">Computer Talk</div>
<div class="NavContent" style="text-align: left;">The above data is available with the [http://www.wolfram.com/ Mathematica] package [[The Mathematica Package KnotTheory`|<code>KnotTheory`</code>]]. Your input (in <font color=red>red</font>) 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 <tt>KnotTheory`</tt> date)
<div class="NavFrame">
<div class="NavHead"><b>Computer Talk.</b>&nbsp;&nbsp;&nbsp;</div>
<div class="NavContent">
The above data is available with the [http://www.wolfram.com/ Mathematica] package [[The Mathematica Package KnotTheory`|<code>KnotTheory`</code>]]. Your input (in <font color=red>red</font>) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
<!-- The following is meant to be similar to the notebook in http://katlas.math.toronto.edu/svn/KnotAtlas/RolfsenKnotPageSession.nb -->

(The path below will be different on your system, and possibly also the <tt>KnotTheory`</tt> date)


{{In|n=1|in=<nowiki>AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
{{In|n=1|in=<nowiki>AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
Line 12: Line 9:


{{Print|Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
{{Print|Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.}}
Read more at http://katlas.org/wiki/KnotTheory.}}


{|
{|
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|width=70px|<code style="color: blue; border: 0px; padding: 0em">In[3]:=</code>
|width=70px|<code style="color: blue; border: 0px; padding: 0em">In[3]:=</code>
|<code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);">K = Knot["{{PAGENAME}}"];</code>
|<code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);">K = Knot["{{PAGENAME}}"];</code>
|}

{{In|n=4|in=<nowiki>PD[K]</nowiki>}}

{{Message|KnotTheory::loading: Loading precomputed data in PD4Knots`.}}

{{FreeStyleOut|4}}
|{{Data:{{PAGENAME}}/PD Presentation}}
|}

{{In|n=5|in=<nowiki>GaussCode[K]</nowiki>}}

{{FreeStyleOut|5}}
| {{Data:{{PAGENAME}}/Gauss Code}}
|}

{{In|n=6|in=<nowiki>DTCode[K]</nowiki>}}

{{FreeStyleOut|6}}
|{{Data:{{PAGENAME}}/DT Code}}
|}

(The path below may be different on your system)

{{In|n=7|in=<nowiki>AppendTo[$Path, "C:/bin/LinKnot/"];</nowiki>}}

{{In|n=8|in=<nowiki>ConwayNotation[K]</nowiki>}}

{{FreeStyleOut|8}}
|{{Data:{{PAGENAME}}/Conway Notation}}
|}

{{In|n=9|in=<nowiki>br = BR[K]</nowiki>}}

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

{{FreeStyleOut|9}}
| <tt>{{Data:{{PAGENAME}}/BraidWord}}</tt>
|}

{{In|n=10|in=<nowiki>{First[br], Crossings[br], BraidIndex[K]}</nowiki>}}

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

{{Message|KnotTheory::loading: Loading precomputed data in IndianaData`.}}

{{FreeStyleOut|10}}
| { {{Data:{{PAGENAME}}/MinimalBraidWidth}}, {{Data:{{PAGENAME}}/MinimalBraidLength}}, {{Data:{{PAGENAME}}/BraidIndex}} }
|}

{{In|n=11|in=<nowiki>Show[BraidPlot[br]]</nowiki>}}

{|
|- align=left valign=top
|width=70px|
|{{Data:{{PAGENAME}}/BraidPlot}}
|}

{{FreeStyleOut|11}}
| <tt>-Graphics-</tt>
|}

{{In|n=12|in=<nowiki>Show[DrawMorseLink[K]]</nowiki>}}

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

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

{|
|- align=left valign=top
|width=70px|
|[[Image:{{PAGENAME}}_ML.gif]]
|}

{{FreeStyleOut|12}}
| <tt>-Graphics-</tt>
|}

{{In|n=13|in=<nowiki>ap = ArcPresentation[K]</nowiki>}}

{{FreeStyleOut|13}}
| <tt>ArcPresentation{{Data:{{PAGENAME}}/Arc Presentation}}</tt>
|}

{{In|n=14|in=<nowiki>Draw[ap]</nowiki>}}

{|
|- align=left valign=top
|width=70px|
|[[Image:{{PAGENAME}}_AP.gif]]
|}

{{FreeStyleOut|14}}
| <tt>-Graphics-</tt>
|}
|}


Latest revision as of 16:36, 2 December 2007

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

Computer Talk
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-
Retrieved from "https://katlas.org/index.php?title=Template:Rolfsen_Knot_Presentations_Computer_Talk&oldid=1691293"