Template:Similar Knots: Difference between revisions

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m (Reverted edits by 221.232.159.112 (Talk); changed back to last version by Drorbn)
 
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Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>):
Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>):
{{{{same_jones}}}}
{{{{same_jones}}}}

⚫
</div>
<div class="NavFrame"><div class="NavHead">Computer Talk</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 may be different on your system, and possibly also the <tt>KnotTheory`</tt> date)

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

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

{|
|- align=left valign=top
|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>
|}

{{In|n=4|in=<nowiki>{A = Alexander[K][t], J = Jones[K][q]}</nowiki>}}

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

{{Message|KnotTheory::loading: Loading precomputed data in Jones4Knots`.}}

{{FreeStyleOut|4}}
| { {{Data:{{PAGENAME}}/Alexander Polynomial}}, {{Data:{{PAGENAME}}/Jones Polynomial}} }
|}

{{In|n=5|in=<nowiki>DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]</nowiki>}}

{{Message|KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.}}

{{Message|KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.}}

{{FreeStyleOut|5}}
| {{{{same_alexander}}}}
|}

{{In|n=6|in=<nowiki>DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]</nowiki>}}

{{Message|KnotTheory::loading: Loading precomputed data in Jones4Knots11`.}}

{{FreeStyleOut|6}}
| {{{{same_jones}}}}
|}
⚫
</div></div>

Latest revision as of 09:21, 13 August 2007

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {{{{same_alexander}}}}

Same Jones Polynomial (up to mirroring, ): {{{{same_jones}}}}

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.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["Similar Knots"];
In[4]:= {A = Alexander[K][t], J = Jones[K][q]}
KnotTheory::loading: Loading precomputed data in PD4Knots`.
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[4]= { Data:Similar Knots/Alexander Polynomial, Data:Similar Knots/Jones Polynomial }
In[5]:= DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
Out[5]= {{{{same_alexander}}}}
In[6]:= DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
Out[6]= {{{{same_jones}}}}
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