K11a216

K11a216 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["K11a216"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 6t3−17t2 + 31t−37 + 31t−1−17t−2 + 6t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−2z6−z4 + z2 + 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]=

{1}

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 147, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q8 + 4q7−9q6 + 15q5−21q4 + 24q3−23q2 + 21q−15 + 9q−1−4q−2 + q−3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z8a−2−5z6a−2 + 2z6a−4 + z6−10z4a−2 + 7z4a−4−z4a−6 + 3z4−8z2a−2 + 8z2a−4−2z2a−6 + 3z2−a−2 + 2a−4−a−6 + 1

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

2z10a−2 + 2z10a−4 + 6z9a−1 + 13z9a−3 + 7z9a−5 + 15z8a−2 + 18z8a−4 + 10z8a−6 + 7z8 + 4az7−4z7a−1−16z7a−3 + 8z7a−7 + a2z6−44z6a−2−47z6a−4−15z6a−6 + 4z6a−8−15z6−9az5−13z5a−1−9z5a−3−18z5a−5−12z5a−7 + z5a−9−2a2z4 + 38z4a−2 + 41z4a−4 + 10z4a−6−5z4a−8 + 10z4 + 6az3 + 12z3a−1 + 16z3a−3 + 18z3a−5 + 7z3a−7−z3a−9 + a2z2−15z2a−2−15z2a−4−4z2a−6 + z2a−8−4z2−az−3za−1−4za−3−4za−5−2za−7 + a−2 + 2a−4 + a−6 + 1

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["K11a216"];

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]=

{ −t4 + 6t3−17t2 + 31t−37 + 31t−1−17t−2 + 6t−3−t−4, −q8 + 4q7−9q6 + 15q5−21q4 + 24q3−23q2 + 21q−15 + 9q−1−4q−2 + q−3 }

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]=

{K11a196, K11a286,}

In[6]:=

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

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

Out[6]=

{K11a196,}