Template:Polynomial Invariants: Difference between revisions
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===Polynomial invariants=== |
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<table width=98%> |
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<tr valign=top> |
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<td>'''[[The Alexander-Conway Polynomial|Alexander polynomial]]'''</td> |
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<td>{{Data:{{PAGENAME}}/Alexander Polynomial}}</td> |
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</tr> |
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<tr valign=top> |
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<td>'''[[The Alexander-Conway Polynomial|Conway polynomial]]'''</td> |
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<td>{{Data:{{PAGENAME}}/Conway Polynomial}}</td> |
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</tr> |
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<tr valign=top> |
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<td>'''[[The Alexander-Conway Polynomial|2nd Alexander ideal]] ([[Data:{{PAGENAME}}/2nd AlexanderIdeal|db]], [[Alexander ideals data sources|data sources]])'''</td> |
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<td>{{Data:{{PAGENAME}}/2nd AlexanderIdeal}}</td> |
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</tr> |
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<tr valign=top> |
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<td>'''[[The Determinant and the Signature|Determinant and Signature]]'''</td> |
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<td>{ {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }</td> |
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</tr><tr valign=top> |
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<td>'''[[The Jones Polynomial|Jones polynomial]]'''</td> |
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<td>{{Data:{{PAGENAME}}/Jones Polynomial}}</td> |
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</tr><tr valign=top> |
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<td>'''[[The HOMFLY-PT Polynomial|HOMFLY-PT polynomial]]''' ([[Data:{{PAGENAME}}/HOMFLYPT Polynomial|db]], [[HOMFLY-PT polynomial data sources|data sources]])</td> |
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<td>{{Data:{{PAGENAME}}/HOMFLYPT Polynomial}}</td> |
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</tr><tr valign=top> |
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<td>'''[[The Kauffman Polynomial|Kauffman polynomial]]''' ([[Data:{{PAGENAME}}/Kauffman Polynomial|db]], [[Kauffman polynomial data sources|data sources]])</td> |
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<td>{{Data:{{PAGENAME}}/Kauffman Polynomial}}</td> |
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</tr> |
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<!--<tr valign=top> |
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<td>'''[[User:Ben/KRhomology|Khovanov-Rozansky polynomial]]'''</td> |
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<td>{{Data:{{PAGENAME}}/Khovanov Rozansky Polynomial}}</td> |
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</tr>--> |
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<tr valign=top> |
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<td>'''[[Quantum knot invariants|The A2 invariant]]'''</td> |
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<td>{{Data:{{PAGENAME}}/QuantumInvariant/A2/1,0}}</td> |
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</tr> |
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<tr valign=top> |
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<td>'''[[Quantum knot invariants|The G2 invariant]]'''</td> |
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<td>{{Data:{{PAGENAME}}/QuantumInvariant/G2/1,0}}</td> |
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</tr> |
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</table> |
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<div class="NavFrame"><div class="NavHead">[[Quantum knot invariants|Further Quantum Invariants]]</div> |
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<div class="NavContent">{{:{{PAGENAME}} Quantum Invariants|quantum invariants}}. |
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</div></div> |
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<div class="NavFrame"><div class="NavHead">Computer Talk</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>]], as shown in the (simulated) Mathematica session below. 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. This Mathematica session is also available (albeit only for the knot [[5_2]]) as the notebook [http://katlas.math.toronto.edu/svn/KnotAtlas/PolynomialInvariantsSession.nb PolynomialInvariantsSession.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 August 31, 2006, 11:25:27.5625. |
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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>Alexander[K][t]</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in PD4Knots`.}} |
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{{FreeStyleOut|4}} |
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| {{Data:{{PAGENAME}}/Alexander Polynomial}} |
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|} |
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{{In|n=5|in=<nowiki>Conway[K][z]</nowiki>}} |
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{{FreeStyleOut|5}} |
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| {{Data:{{PAGENAME}}/Conway Polynomial}} |
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|} |
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{{In|n=6|in=<nowiki>Alexander[K, 2][t]</nowiki>}} |
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{{Message|KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.}} |
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{{FreeStyleOut|6}} |
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| {{Data:{{PAGENAME}}/2nd AlexanderIdeal}} |
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|} |
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{{In|n=7|in=<nowiki>{KnotDet[K], KnotSignature[K]}</nowiki>}} |
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{{FreeStyleOut|7}} |
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| { {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} } |
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|} |
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{{In|n=8|in=<nowiki>Jones[K][q]</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in Jones4Knots`.}} |
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{{FreeStyleOut|8}} |
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| {{Data:{{PAGENAME}}/Jones Polynomial}} |
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|} |
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{{In|n=9|in=<nowiki>HOMFLYPT[K][a, z]</nowiki>}} |
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{{Message|KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.}} |
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{{FreeStyleOut|9}} |
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| {{Data:{{PAGENAME}}/HOMFLYPT Polynomial}} |
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|} |
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{{In|n=10|in=<nowiki>Kauffman[K][a, z]</nowiki>}} |
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{{Message|KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.}} |
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{{FreeStyleOut|10}} |
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| {{Data:{{PAGENAME}}/Kauffman Polynomial}} |
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|} |
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</div></div> |
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Revision as of 18:18, 14 August 2007
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