Template:Polynomial Invariants: Difference between revisions

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<div style="border: solid pink 1px">
<div style="border: solid pink 1px">
===Polynomial invariants===
===Polynomial invariants===
<table width=98%>
<table width=98%>
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<td>'''[[The Alexander-Conway Polynomial|Alexander polynomial]]'''</td>
<td>'''[[The Alexander-Conway Polynomial|Alexander polynomial]]'''</td>
<td>{{Data:{{PAGENAME}}/Alexander Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/Alexander Polynomial}}</td>
</tr><tr valign=top>
</tr>
<tr valign=top>
<td>'''[[The Alexander-Conway Polynomial|Conway polynomial]]'''</td>
<td>'''[[The Alexander-Conway Polynomial|Conway polynomial]]'''</td>
<td>{{Data:{{PAGENAME}}/Conway Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/Conway Polynomial}}</td>
</tr><tr valign=top>
</tr>
<tr valign=top>
<td>'''[[The Alexander-Conway Polynomial|2nd Alexander ideal]] ([[Data:{{PAGENAME}}/2nd AlexanderIdeal|db]], [[Alexander ideals data sources|data sources]])'''</td>
<td>{{Data:{{PAGENAME}}/2nd AlexanderIdeal}}</td>
</tr>
<tr valign=top>
<td>'''[[The Determinant and the Signature|Determinant and Signature]]'''</td>
<td>'''[[The Determinant and the Signature|Determinant and Signature]]'''</td>
<td>{ {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }</td>
<td>{ {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }</td>
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<td>{{Data:{{PAGENAME}}/HOMFLYPT Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/HOMFLYPT Polynomial}}</td>
</tr><tr valign=top>
</tr><tr valign=top>
<td>'''[[The Kauffman Polynomial|Kauffman polynomial]]'''</td>
<td>'''[[The Kauffman Polynomial|Kauffman polynomial]]''' ([[Data:{{PAGENAME}}/Kauffman Polynomial|db]], [[Kauffman polynomial data sources|data sources]])</td>
<td>{{Data:{{PAGENAME}}/Kauffman Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/Kauffman Polynomial}}</td>
</tr>
</tr>
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</table>
</table>


<div class="NavFrame"><div class="NavHead">'''[[Quantum knot invariants|Further Quantum Invariants.]]'''&nbsp;&nbsp;&nbsp;</div>
<div class="NavFrame"><div class="NavHead">Further Quantum Invariants</div>
<div class="NavContent">{{:{{PAGENAME}} Quantum Invariants|quantum invariants}}.
<div class="NavContent">{{:{{PAGENAME}} Quantum Invariants|quantum invariants}}.
</div></div>
</div></div>


<div class="NavFrame"><div class="NavHead"><b>Computer Talk.</b>&nbsp;&nbsp;&nbsp;</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.
<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].
<!-- 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)
(The path below may be different on your system, and possibly also the <tt>KnotTheory`</tt> date)
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<< KnotTheory`</nowiki>}}
<< KnotTheory`</nowiki>}}


{{Print|Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
{{Print|Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.}}
Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.}}


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|}
|}


{{In|n=6|in=<nowiki>{KnotDet[K], KnotSignature[K]}</nowiki>}}
{{In|n=6|in=<nowiki>Alexander[K, 2][t]</nowiki>}}

{{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.}}


{{FreeStyleOut|6}}
{{FreeStyleOut|6}}
| {{Data:{{PAGENAME}}/2nd AlexanderIdeal}}
|}

{{In|n=7|in=<nowiki>{KnotDet[K], KnotSignature[K]}</nowiki>}}

{{FreeStyleOut|7}}
| { {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }
| { {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }
|}
|}


{{In|n=7|in=<nowiki>Jones[K][q]</nowiki>}}
{{In|n=8|in=<nowiki>Jones[K][q]</nowiki>}}


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


{{FreeStyleOut|7}}
{{FreeStyleOut|8}}
| {{Data:{{PAGENAME}}/Jones Polynomial}}
| {{Data:{{PAGENAME}}/Jones Polynomial}}
|}
|}


{{In|n=8|in=<nowiki>HOMFLYPT[K][a, z]</nowiki>}}
{{In|n=9|in=<nowiki>HOMFLYPT[K][a, z]</nowiki>}}


{{Message|KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.}}
{{Message|KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.}}


{{FreeStyleOut|8}}
{{FreeStyleOut|9}}
| {{Data:{{PAGENAME}}/HOMFLYPT Polynomial}}
| {{Data:{{PAGENAME}}/HOMFLYPT Polynomial}}
|}
|}


{{In|n=9|in=<nowiki>Kauffman[K][a, z]</nowiki>}}
{{In|n=10|in=<nowiki>Kauffman[K][a, z]</nowiki>}}


{{Message|KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.}}
{{Message|KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.}}


{{FreeStyleOut|9}}
{{FreeStyleOut|10}}
| {{Data:{{PAGENAME}}/Kauffman Polynomial}}
| {{Data:{{PAGENAME}}/Kauffman Polynomial}}
|}
|}

Latest revision as of 12:53, 1 December 2007

Polynomial invariants

Alexander polynomial Data:Polynomial Invariants/Alexander Polynomial
Conway polynomial Data:Polynomial Invariants/Conway Polynomial
2nd Alexander ideal (db, data sources) Data:Polynomial Invariants/2nd AlexanderIdeal
Determinant and Signature { Data:Polynomial Invariants/Determinant, Data:Polynomial Invariants/Signature }
Jones polynomial Data:Polynomial Invariants/Jones Polynomial
HOMFLY-PT polynomial (db, data sources) Data:Polynomial Invariants/HOMFLYPT Polynomial
Kauffman polynomial (db, data sources) Data:Polynomial Invariants/Kauffman Polynomial
The A2 invariant Data:Polynomial Invariants/QuantumInvariant/A2/1,0
The G2 invariant Data:Polynomial Invariants/QuantumInvariant/G2/1,0
Further Quantum Invariants
Polynomial Invariants Quantum Invariants.
Computer Talk
The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) 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 PolynomialInvariantsSession.nb.

(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 August 31, 2006, 11:25:27.5625.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["Polynomial Invariants"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= Data:Polynomial Invariants/Alexander Polynomial
In[5]:= Conway[K][z]
Out[5]= Data:Polynomial Invariants/Conway Polynomial
In[6]:= Alexander[K, 2][t]
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.
Out[6]= Data:Polynomial Invariants/2nd AlexanderIdeal
In[7]:= {KnotDet[K], KnotSignature[K]}
Out[7]= { Data:Polynomial Invariants/Determinant, Data:Polynomial Invariants/Signature }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= Data:Polynomial Invariants/Jones Polynomial
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= Data:Polynomial Invariants/HOMFLYPT Polynomial
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= Data:Polynomial Invariants/Kauffman Polynomial
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