K11n46

K11n46 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["K11n46"];

In[4]:=

Alexander[K][t]

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

Out[4]=

2t3−8t2 + 18t−23 + 18t−1−8t−2 + 2t−3

In[5]:=

Conway[K][z]

Out[5]=

2z6 + 4z4 + 4z2 + 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]=

{ 79, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

q9−4q8 + 7q7−11q6 + 13q5−13q4 + 13q3−9q2 + 6q−2

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

2z6a−4−2z4a−2 + 9z4a−4−3z4a−6−4z2a−2 + 15z2a−4−8z2a−6 + z2a−8−2a−2 + 8a−4−6a−6 + a−8

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

2z9a−5 + 2z9a−7 + 6z8a−4 + 11z8a−6 + 5z8a−8 + 5z7a−3 + 8z7a−5 + 7z7a−7 + 4z7a−9 + z6a−2−14z6a−4−27z6a−6−11z6a−8 + z6a−10−9z5a−3−30z5a−5−32z5a−7−11z5a−9 + 6z4a−2 + 23z4a−4 + 22z4a−6 + 3z4a−8−2z4a−10 + 3z3a−1 + 15z3a−3 + 32z3a−5 + 28z3a−7 + 8z3a−9−6z2a−2−20z2a−4−15z2a−6 + z2a−10−2za−1−7za−3−13za−5−9za−7−za−9 + 2a−2 + 8a−4 + 6a−6 + a−8

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["K11n46"];

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]=

{ 2t3−8t2 + 18t−23 + 18t−1−8t−2 + 2t−3, q9−4q8 + 7q7−11q6 + 13q5−13q4 + 13q3−9q2 + 6q−2 }

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]=

{10_57, K11n40,}

In[6]:=

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

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

Out[6]=

{K11n40,}