K11a357

K11a357 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["K11a357"];

In[4]:=

Alexander[K][t]

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

Out[4]=

4t3−11t2 + 19t−23 + 19t−1−11t−2 + 4t−3

In[5]:=

Conway[K][z]

Out[5]=

4z6 + 13z4 + 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]=

{ 91, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q14 + 3q13−7q12 + 10q11−13q10 + 15q9−14q8 + 12q7−8q6 + 5q5−2q4 + 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 + 8z4a−8 + 2z4a−10−z4a−12 + 4z2a−6 + 10z2a−8−z2a−10−2z2a−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 + 5z9a−11 + 3z9a−13 + 3z8a−8 + 2z8a−10 + 4z8a−12 + 5z8a−14 + 2z7a−7−2z7a−9−10z7a−11−z7a−13 + 5z7a−15 + z6a−6−10z6a−8−7z6a−10−7z6a−12−8z6a−14 + 3z6a−16−6z5a−7−2z5a−9 + 11z5a−11−3z5a−13−9z5a−15 + z5a−17−4z4a−6 + 15z4a−8 + 10z4a−10 + z4a−12 + 5z4a−14−5z4a−16 + 4z3a−7 + 2z3a−9−6z3a−11 + 3z3a−13 + 5z3a−15−2z3a−17 + 4z2a−6−14z2a−8−9z2a−10 + 6z2a−12−2z2a−14 + z2a−16−2za−9 + 2za−11−3za−15 + za−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["K11a357"];

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]=

{ 4t3−11t2 + 19t−23 + 19t−1−11t−2 + 4t−3, −q14 + 3q13−7q12 + 10q11−13q10 + 15q9−14q8 + 12q7−8q6 + 5q5−2q4 + 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]=

{}