Template:Rolfsen Knot Page
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[[Image:8_16.{{{ext}}}|80px|link=8_16]] |
[[Image:8_18.{{{ext}}}|80px|link=8_18]] |
Visit Rolfsen Knot Page's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)
Visit [{{{KnotilusURL}}} Rolfsen Knot Page's page] at Knotilus!
Visit Rolfsen Knot Page's page at the original Knot Atlas!
Knot presentations
Three dimensional invariants
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[edit Notes for Rolfsen Knot Page's three dimensional invariants] |
Polynomial invariants
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]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["Rolfsen Knot Page"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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Data:Rolfsen Knot Page/Alexander Polynomial |
In[5]:=
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Conway[K][z]
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Out[5]=
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Data:Rolfsen Knot Page/Conway Polynomial |
In[6]:=
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Alexander[K, 2][t]
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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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Out[6]=
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Data:Rolfsen Knot Page/2nd AlexanderIdeal |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ Data:Rolfsen Knot Page/Determinant, Data:Rolfsen Knot Page/Signature } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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Data:Rolfsen Knot Page/Jones Polynomial |
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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Data:Rolfsen Knot Page/HOMFLYPT Polynomial |
In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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Data:Rolfsen Knot Page/Kauffman Polynomial |
Vassiliev invariants
| V2 and V3: | (Data:Rolfsen Knot Page/V 2, Data:Rolfsen Knot Page/V 3) |
| V2,1 through V6,9: |
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
