A Sample KnotTheory` Session: Difference between revisions

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<!--$$<< KnotTheory`$$-->
<!--$$<< KnotTheory`$$-->
<!--Robot Land, no human edits to "END"-->
<!--Robot Land, no human edits to "END"-->
<tt><font color=blue>In[2]:=</font></tt><code> << KnotTheory`</code>
<tt><font color=blue>In[1]:=</font></tt><code> << KnotTheory`</code>


<tt>Loading KnotTheory` (version of September 14, 2005, 13:37:36)...</tt>
<tt>Loading KnotTheory` (version of September 14, 2005, 13:37:36)...</tt>
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<!--Robot Land, no human edits to "END"-->
<!--Robot Land, no human edits to "END"-->
{{In|
{{In|
n = 3 |
n = 2 |
in = <nowiki>K = Knot[8, 17];
in = <nowiki>K = Knot[8, 17];
K11 = Knot[11, Alternating, 231];
K11 = Knot[11, Alternating, 231];
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<!--Robot Land, no human edits to "END"-->
<!--Robot Land, no human edits to "END"-->
{{InOut|
{{InOut|
n = 4 |
n = 3 |
in = <nowiki>PD[K]</nowiki> |
in = <nowiki>PD[K]</nowiki> |
out= <nowiki>PD[X[6, 2, 7, 1], X[14, 8, 15, 7], X[8, 3, 9, 4], X[2, 13, 3, 14],
out= <nowiki>PD[X[6, 2, 7, 1], X[14, 8, 15, 7], X[8, 3, 9, 4], X[2, 13, 3, 14],
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<!--Robot Land, no human edits to "END"-->
<!--Robot Land, no human edits to "END"-->
{{InOut|
{{InOut|
n = 5 |
n = 4 |
in = <nowiki>{GaussCode[K], GaussCode[L]}</nowiki> |
in = <nowiki>{GaussCode[K], GaussCode[L]}</nowiki> |
out= <nowiki>{GaussCode[1, -4, 3, -6, 5, -1, 2, -3, 6, -8, 7, -5, 4, -2, 8, -7],
out= <nowiki>{GaussCode[1, -4, 3, -6, 5, -1, 2, -3, 6, -8, 7, -5, 4, -2, 8, -7],
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<!--Robot Land, no human edits to "END"-->
<!--Robot Land, no human edits to "END"-->
{{InOut|
{{InOut|
n = 6 |
n = 5 |
in = <nowiki>DTCode[K]</nowiki> |
in = <nowiki>DTCode[K]</nowiki> |
out= <nowiki>DTCode[6, 8, 12, 14, 4, 16, 2, 10]</nowiki>}}
out= <nowiki>DTCode[6, 8, 12, 14, 4, 16, 2, 10]</nowiki>}}
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<!--$$br = BR[K]$$-->
<!--$$br = BR[K]$$-->
<!--Robot Land, no human edits to "END"-->
{{InOut|
n = 6 |
in = <nowiki>br = BR[K]</nowiki> |
out= <nowiki>BR[3, {-1, -1, 2, -1, 2, -1, 2, 2}]</nowiki>}}
<!--END-->
<!--END-->


<!--$$Show[BraidPlot[br]]$$-->
<!--$$Show[BraidPlot[br]]$$-->
<!--Robot Land, no human edits to "END"-->
{{Graphics|
n = 7 |
in = <nowiki>Show[BraidPlot[br]]</nowiki> |
img= A_Sample_KnotTheory%60_Session_Out_7.gif |
out= <nowiki>-Graphics-</nowiki>}}
<!--END-->
<!--END-->


<!--$${First[br], Crossings[br], BraidIndex[K]}$$-->
<!--$${First[br], Crossings[br], BraidIndex[K]}$$-->
<!--Robot Land, no human edits to "END"-->
{{InOut|
n = 8 |
in = <nowiki>{First[br], Crossings[br], BraidIndex[K]}</nowiki> |
out= <nowiki>{3, 8, 3}</nowiki>}}
<!--END-->
<!--END-->

Revision as of 15:06, 18 September 2005


KnotTheory`/Navigation 

The Mathematica Package KnotTheory`

Setup

The first step is to load KnotTheory` as in Setup:

In[1]:= << KnotTheory`

Loading KnotTheory` (version of September 14, 2005, 13:37:36)...

8 17.gif
8_17 		K11a231.gif
K11a231
L8n6.gif
L8n6 		T(7,5).jpg
T(7,5)

Let us now introduce the four star knots that will accompany us throughout this session:

In[2]:= K = Knot[8, 17]; K11 = Knot[11, Alternating, 231]; L = Link[8, NonAlternating, 6]; TK = TorusKnot[7,5];

Presentations

In[3]:= PD[K]
Out[3]= PD[X[6, 2, 7, 1], X[14, 8, 15, 7], X[8, 3, 9, 4], X[2, 13, 3, 14], X[12, 5, 13, 6], X[4, 9, 5, 10], X[16, 12, 1, 11], X[10, 16, 11, 15]]
In[4]:= {GaussCode[K], GaussCode[L]}
Out[4]= {GaussCode[1, -4, 3, -6, 5, -1, 2, -3, 6, -8, 7, -5, 4, -2, 8, -7], GaussCode[{1, -7, 2, -8}, {-5, 4, -6, 3}, {7, -1, -4, 5, 8, -2, -3, 6}]}
In[5]:= DTCode[K]
Out[5]= DTCode[6, 8, 12, 14, 4, 16, 2, 10]
In[6]:= br = BR[K]
Out[6]= BR[3, {-1, -1, 2, -1, 2, -1, 2, 2}]
In[7]:= Show[BraidPlot[br]]
File:A Sample KnotTheory` Session Out 7.gif
Out[7]= -Graphics-
In[8]:= {First[br], Crossings[br], BraidIndex[K]}
Out[8]= {3, 8, 3}
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