K11n152

K11n152 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["K11n152"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−2t2 + 6t−7 + 6t−1−2t−2

In[5]:=

Conway[K][z]

Out[5]=

−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]=

{1}

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 23, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q8 + 3q7−4q6 + 5q5−5q4 + 4q3−3q2 + q + 1−q−1 + q−2

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z6a−2 + z6a−4−7z4a−2 + 5z4a−4−z4a−6 + z4−13z2a−2 + 9z2a−4−2z2a−6 + 4z2−7a−2 + 5a−4−a−6 + 4

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z9a−1 + z9a−3 + 2z8a−2 + 2z8a−4 + z8a−6 + z8−7z7a−1−7z7a−3 + 3z7a−5 + 3z7a−7−17z6a−2−13z6a−4 + 3z6a−8−7z6 + 13z5a−1 + 11z5a−3−11z5a−5−8z5a−7 + z5a−9 + 40z4a−2 + 28z4a−4−5z4a−6−8z4a−8 + 15z4−7z3a−1 + 2z3a−3 + 15z3a−5 + 4z3a−7−2z3a−9−31z2a−2−19z2a−4 + 2z2a−6 + 3z2a−8−13z2−4za−3−6za−5−2za−7 + 7a−2 + 5a−4 + a−6 + 4

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["K11n152"];

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]=

{ −2t2 + 6t−7 + 6t−1−2t−2, −q8 + 3q7−4q6 + 5q5−5q4 + 4q3−3q2 + q + 1−q−1 + q−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]=

{8_6, K11n20, K11n151,}

In[6]:=

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

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

Out[6]=

{K11n151,}