Template:Polynomial Invariants: Difference between revisions

From Knot Atlas
Jump to navigationJump to search
No edit summary
No edit summary
Line 21: Line 21:
<td>{{Data:{{PAGENAME}}/Kauffman Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/Kauffman Polynomial}}</td>
</tr>
</tr>
<tr valign=top>
<!--<tr valign=top>
<td>'''[[User:Ben/KRhomology|Khovanov-Rozansky polynomial]]'''</td>
<td>'''[[User:Ben/KRhomology|Khovanov-Rozansky polynomial]]'''</td>
<td>{{Data:{{PAGENAME}}/Khovanov Rozansky Polynomial}}</td>
<td>{{Data:{{PAGENAME}}/Khovanov Rozansky Polynomial}}</td>
</tr>
</tr>-->
<tr valign=top>
<tr valign=top>
<td>'''[[Quantum knot invariants|The A2 invariant]]'''</td>
<td>'''[[Quantum knot invariants|The A2 invariant]]'''</td>
Line 65: Line 65:
|}
|}


{{In|n=5|in=<nowiki>Conway[K][t]</nowiki>}}
{{In|n=5|in=<nowiki>Conway[K][z]</nowiki>}}


{{FreeStyleOut|5}}
{{FreeStyleOut|5}}
Line 75: Line 75:
{{FreeStyleOut|6}}
{{FreeStyleOut|6}}
| { {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }
| { {{Data:{{PAGENAME}}/Determinant}}, {{Data:{{PAGENAME}}/Signature}} }
|}


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

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

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

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

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

{{FreeStyleOut|9}}
| {{Data:{{PAGENAME}}/Kauffman Polynomial}}
|}
|}
</div></div>
</div></div>

Revision as of 17:22, 24 June 2006

Polynomial invariants

Alexander polynomial Data:Polynomial Invariants/Alexander Polynomial
Conway polynomial Data:Polynomial Invariants/Conway Polynomial
Determinant and Signature { Data:Polynomial Invariants/Determinant, Data:Polynomial Invariants/Signature }
Jones polynomial Data:Polynomial Invariants/Jones Polynomial
HOMFLY-PT polynomial Data:Polynomial Invariants/HOMFLYPT Polynomial
Kauffman polynomial 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`. 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["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]:= {KnotDet[K], KnotSignature[K]}
Out[6]= { Data:Polynomial Invariants/Determinant, Data:Polynomial Invariants/Signature }


In[7]:= Jones[K][q]
Out[7]= Data:Polynomial Invariants/Jones Polynomial
In[8]:= HOMFLYPT[K][a, z]
Out[8]= Data:Polynomial Invariants/HOMFLYPT Polynomial
In[9]:= Kauffman[K][a, z]
Out[9]= Data:Polynomial Invariants/Kauffman Polynomial
Retrieved from "https://katlas.org/index.php?title=Template:Polynomial_Invariants&oldid=50452"