K11n133

K11n133 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["K11n133"];

In[4]:=

Alexander[K][t]

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

Out[4]=

t4−4t3 + 6t2−2t−1−2t−1 + 6t−2−4t−3 + t−4

In[5]:=

Conway[K][z]

Out[5]=

z8 + 4z6 + 2z4 + 2z2 + 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]=

{5,t + 1}

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 25, 4 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q7 + 2q6−3q5 + 4q4−4q3 + 4q2−3q + 3−q−1

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z8a−4−z6a−2 + 6z6a−4−z6a−6−4z4a−2 + 11z4a−4−5z4a−6−2z2a−2 + 8z2a−4−5z2a−6 + z2a−8 + a−2 + a−4−a−6

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

2z9a−3 + 2z9a−5 + 3z8a−2 + 6z8a−4 + 3z8a−6 + z7a−1−8z7a−3−8z7a−5 + z7a−7−15z6a−2−31z6a−4−16z6a−6−4z5a−1 + 3z5a−3 + 2z5a−5−5z5a−7 + 19z4a−2 + 42z4a−4 + 23z4a−6 + 3z3a−1 + 7z3a−3 + 10z3a−5 + 6z3a−7−6z2a−2−16z2a−4−11z2a−6−z2a−8−za−1−3za−3−5za−5−3za−7−a−2 + a−4 + a−6

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["K11n133"];

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]=

{ t4−4t3 + 6t2−2t−1−2t−1 + 6t−2−4t−3 + t−4, −q7 + 2q6−3q5 + 4q4−4q3 + 4q2−3q + 3−q−1 }

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]=

{K11n50, K11n132,}