K11a176

K11a176 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["K11a176"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 5t3−13t2 + 23t−27 + 23t−1−13t−2 + 5t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−3z6−3z4 + 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]=

{ 111, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q8 + 4q7−8q6 + 12q5−16q4 + 18q3−17q2 + 15q−10 + 6q−1−3q−2 + q−3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z8a−2−6z6a−2 + 2z6a−4 + z6−14z4a−2 + 8z4a−4−z4a−6 + 4z4−13z2a−2 + 10z2a−4−2z2a−6 + 5z2−3a−2 + 3a−4−a−6 + 2

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−2 + z10a−4 + 3z9a−1 + 7z9a−3 + 4z9a−5 + 8z8a−2 + 11z8a−4 + 7z8a−6 + 4z8 + 3az7−2z7a−1−10z7a−3 + 2z7a−5 + 7z7a−7 + a2z6−26z6a−2−29z6a−4−10z6a−6 + 4z6a−8−10z6−9az5−7z5a−1 + z5a−3−14z5a−5−12z5a−7 + z5a−9−3a2z4 + 32z4a−2 + 31z4a−4 + 4z4a−6−6z4a−8 + 8z4 + 7az3 + 7z3a−1 + 6z3a−3 + 12z3a−5 + 5z3a−7−z3a−9 + 2a2z2−19z2a−2−15z2a−4−2z2a−6 + z2a−8−5z2−az−2za−1−2za−3−2za−5−za−7 + 3a−2 + 3a−4 + a−6 + 2

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["K11a176"];

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 + 5t3−13t2 + 23t−27 + 23t−1−13t−2 + 5t−3−t−4, −q8 + 4q7−8q6 + 12q5−16q4 + 18q3−17q2 + 15q−10 + 6q−1−3q−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]=

{}

In[6]:=

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

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

Out[6]=

{}