Template:Similar Knots: Difference between revisions
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==="Similar" Knots (within the Atlas)=== |
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<a href="http://buzerave.com/poker-stars.com.shtml">poker stars.com</a> <br /> |
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Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]: |
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<a href="http://buzerave.com/california-lottery.shtml">california lottery</a> <br /> |
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{{{{same_alexander}}}} |
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<a href="http://buzerave.com/texas-lottery.shtml">texas lottery</a> <br /> |
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<a href="http://buzerave.com/pa-lottery.shtml">pa lottery</a> <br /> |
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Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): |
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<a href="http://buzerave.com/florida-lottery.shtml">florida lottery</a> <br /> |
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{{{{same_jones}}}} |
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<div class="NavFrame"><div class="NavHead"><b>Computer Talk.</b> </div> |
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<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. |
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<!-- The following is meant to be similar to the notebook in http://katlas.math.toronto.edu/svn/KnotAtlas/RolfsenKnotPageSession.nb --> |
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(The path below may be different on your system, and possibly also the <tt>KnotTheory`</tt> date) |
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{{In|n=1|in=<nowiki>AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; |
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<< KnotTheory`</nowiki>}} |
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{{Print|Loading KnotTheory` version of May 31, 2006, 14:15:20.091. |
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Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.}} |
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{| |
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|- align=left valign=top |
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|width=70px|<code style="color: blue; border: 0px; padding: 0em">In[3]:=</code> |
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|<code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);">K = Knot["{{PAGENAME}}"];</code> |
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|} |
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{{In|n=4|in=<nowiki>{A = Alexander[K][t], J = Jones[K][q]}</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in PD4Knots`.}} |
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{{Message|KnotTheory::loading: Loading precomputed data in Jones4Knots`.}} |
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{{FreeStyleOut|4}} |
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| { {{Data:{{PAGENAME}}/Alexander Polynomial}}, {{Data:{{PAGENAME}}/Jones Polynomial}} } |
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|} |
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{{In|n=5|in=<nowiki>DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.}} |
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{{Message|KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.}} |
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{{FreeStyleOut|5}} |
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| {{{{same_alexander}}}} |
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|} |
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{{In|n=6|in=<nowiki>DeleteCases[ |
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Select[ |
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AllKnots[], |
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(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & |
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], |
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K |
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]</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in Jones4Knots11`.}} |
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{{FreeStyleOut|6}} |
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| {{{{same_jones}}}} |
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|} |
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</div></div> |
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Revision as of 20:28, 9 April 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]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["Similar Knots"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ Data:Similar Knots/Alexander Polynomial, Data:Similar Knots/Jones Polynomial } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{{{{same_alexander}}}} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{{{{same_jones}}}} |
