|
|
Line 1: |
Line 1: |
|
|
{{todo}} Jones polynomial doesn't parse. |
|
|
|
|
{{Template:Basic Knot Invariants|name=9_1}} |
|
{{Template:Basic Knot Invariants|name=9_1}} |
Revision as of 21:58, 24 August 2005
Todo: Jones polynomial doesn't parse.
Polynomial invariants
Alexander polynomial |
|
Conway polynomial |
|
2nd Alexander ideal (db, data sources) |
|
Determinant and Signature |
{ 9, -8 } |
Jones polynomial |
|
HOMFLY-PT polynomial (db, data sources) |
|
Kauffman polynomial (db, data sources) |
|
The A2 invariant |
|
The G2 invariant |
|
Further Quantum Invariants
Further quantum knot invariants for 9_1.
A1 Invariants.
Weight
|
Invariant
|
1
|
|
2
|
|
3
|
|
4
|
|
5
|
|
6
|
|
8
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{720}-q^{704}-q^{702}-q^{700}+q^{670}+q^{668}+q^{666}+q^{664}+q^{662}-q^{618}-q^{616}-q^{614}-q^{612}-q^{610}-q^{608}-q^{606}+q^{548}+q^{546}+q^{544}+q^{542}+q^{540}+q^{538}+q^{536}+q^{534}+q^{532}-q^{460}-q^{458}-q^{456}-q^{454}-q^{452}-q^{450}-q^{448}-q^{446}-q^{444}-q^{442}-q^{440}+q^{354}+q^{352}+q^{350}+q^{348}+q^{346}+q^{344}+q^{342}+q^{340}+q^{338}+q^{336}+q^{334}+q^{332}+q^{330}-q^{230}-q^{228}-q^{226}-q^{224}-q^{222}-q^{220}-q^{218}-q^{216}-q^{214}-q^{212}-q^{210}-q^{208}-q^{206}-q^{204}-q^{202}+q^{88}+q^{86}+q^{84}+q^{82}+q^{80}+q^{78}+q^{76}+q^{74}+q^{72}+q^{70}+q^{68}+q^{66}+q^{64}+q^{62}+q^{60}+q^{58}+q^{56}}
|
A2 Invariants.
Weight
|
Invariant
|
1,0
|
|
1,1
|
|
2,0
|
|
A3 Invariants.
Weight
|
Invariant
|
0,1,0
|
|
1,0,0
|
|
1,0,1
|
|
A4 Invariants.
Weight
|
Invariant
|
0,1,0,0
|
|
1,0,0,0
|
|
B2 Invariants.
Weight
|
Invariant
|
0,1
|
|
1,0
|
|
D4 Invariants.
Weight
|
Invariant
|
0,1,0,0
|
|
1,0,0,0
|
|
G2 Invariants.
Weight
|
Invariant
|
1,0
|
|
.
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`
|
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
|
Out[5]=
|
|
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]=
|
|
In[7]:=
|
{KnotDet[K], KnotSignature[K]}
|
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
|
|
In[9]:=
|
HOMFLYPT[K][a, z]
|
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
|
|
In[10]:=
|
Kauffman[K][a, z]
|
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
|
|