Template:Large Knot Page
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[[Image:Data:Large Knot Page/Previous Knot.gif|80px|link=Data:Large Knot Page/Previous Knot]] |
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Polynomial invariants
Further 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]:=
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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["Large 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:Large Knot Page/Alexander Polynomial |
In[5]:=
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Conway[K][z]
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Out[5]=
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Data:Large 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:Large 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:Large Knot Page/Determinant, Data:Large 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:Large 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:Large 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:Large Knot Page/Kauffman Polynomial |
Khovanov Homology
| The coefficients of the monomials [math]\displaystyle{ t^rq^j }[/math] are shown, along with their alternating sums [math]\displaystyle{ \chi }[/math] (fixed [math]\displaystyle{ j }[/math], alternation over [math]\displaystyle{ r }[/math]). The squares with yellow highlighting are those on the "critical diagonals", where [math]\displaystyle{ j-2r=s+1 }[/math] or [math]\displaystyle{ j-2r=s-1 }[/math], where [math]\displaystyle{ s= }[/math]Data:Large Knot Page/Signature is the signature of Large Knot Page. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:Large Knot Page/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
Data:Large Knot Page/Integral Khovanov Homology |
