Template:Polynomial Invariants
From Knot Atlas
Jump to navigationJump to search
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]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
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 |
