K11a336

K11a336 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["K11a336"];

In[4]:=

Alexander[K][t]

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

Out[4]=

4t3−9t2 + 11t−11 + 11t−1−9t−2 + 4t−3

In[5]:=

Conway[K][z]

Out[5]=

4z6 + 15z4 + 11z2 + 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]=

{ 59, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q14 + 2q13−4q12 + 6q11−8q10 + 9q9−9q8 + 8q7−5q6 + 4q5−2q4 + q3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z6a−6 + 2z6a−8 + z6a−10 + 4z4a−6 + 9z4a−8 + 3z4a−10−z4a−12 + 3z2a−6 + 11z2a−8−3z2a−12 + 4a−8−2a−10−a−12

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−10 + z10a−12 + 2z9a−9 + 4z9a−11 + 2z9a−13 + 3z8a−8−z8a−10−2z8a−12 + 2z8a−14 + 2z7a−7−6z7a−9−17z7a−11−7z7a−13 + 2z7a−15 + z6a−6−13z6a−8−7z6a−10 + z6a−12−4z6a−14 + 2z6a−16−7z5a−7 + 3z5a−9 + 28z5a−11 + 14z5a−13−3z5a−15 + z5a−17−4z4a−6 + 19z4a−8 + 17z4a−10 + 3z4a−12 + 4z4a−14−5z4a−16 + 4z3a−7 + 2z3a−9−15z3a−11−11z3a−13−z3a−15−3z3a−17 + 3z2a−6−15z2a−8−11z2a−10 + 2z2a−12−3z2a−14 + 2z2a−16−2za−9 + 3za−11 + 3za−13 + 2za−17 + 4a−8 + 2a−10−a−12

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["K11a336"];

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]=

{ 4t3−9t2 + 11t−11 + 11t−1−9t−2 + 4t−3, −q14 + 2q13−4q12 + 6q11−8q10 + 9q9−9q8 + 8q7−5q6 + 4q5−2q4 + 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]=

{}