K11a43

K11a43 Quantum Invariants.

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. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["K11a43"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

4t3−15t2 + 30t−37 + 30t−1−15t−2 + 4t−3

In[5]:=

Conway[K][z]

Out[5]=

4z6 + 9z4 + 6z2 + 1

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]}

Out[7]=

{ 135, 6 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

−q14 + 4q13−8q12 + 14q11−20q10 + 21q9−22q8 + 19q7−13q6 + 9q5−3q4 + q3

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

z6a−6 + 3z6a−8 + 3z4a−6 + 12z4a−8−6z4a−10 + 3z2a−6 + 16z2a−8−17z2a−10 + 4z2a−12 + a−6 + 7a−8−12a−10 + 6a−12−a−14

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

z10a−10 + z10a−12 + 4z9a−9 + 8z9a−11 + 4z9a−13 + 6z8a−8 + 16z8a−10 + 17z8a−12 + 7z8a−14 + 3z7a−7 + 4z7a−9 + 7z7a−11 + 13z7a−13 + 7z7a−15 + z6a−6−15z6a−8−41z6a−10−31z6a−12−2z6a−14 + 4z6a−16−6z5a−7−30z5a−9−54z5a−11−41z5a−13−10z5a−15 + z5a−17−3z4a−6 + 18z4a−8 + 38z4a−10 + 12z4a−12−11z4a−14−6z4a−16 + 3z3a−7 + 35z3a−9 + 63z3a−11 + 39z3a−13 + 7z3a−15−z3a−17 + 3z2a−6−16z2a−8−27z2a−10−3z2a−12 + 8z2a−14 + 3z2a−16−15za−9−27za−11−15za−13−3za−15−a−6 + 7a−8 + 12a−10 + 6a−12 + a−14

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["K11a43"];

In[4]:=

{A = Alexander[K][t], J = Jones[K][q]}

KnotTheory::loading: Loading precomputed data in PD4Knots`.

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[4]=

{ 4t3−15t2 + 30t−37 + 30t−1−15t−2 + 4t−3, −q14 + 4q13−8q12 + 14q11−20q10 + 21q9−22q8 + 19q7−13q6 + 9q5−3q4 + q3 }

In[5]:=

DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]

KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.

KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.

Out[5]=

{}

In[6]:=

DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]

KnotTheory::loading: Loading precomputed data in Jones4Knots11`.

Out[6]=

{}