K11a245

K11a245 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["K11a245"];

In[4]:=

Alexander[K][t]

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

Out[4]=

3t3−9t2 + 16t−19 + 16t−1−9t−2 + 3t−3

In[5]:=

Conway[K][z]

Out[5]=

3z6 + 9z4 + 7z2 + 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]=

{ 75, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q14 + 3q13−6q12 + 9q11−11q10 + 12q9−12q8 + 9q7−6q6 + 4q5−q4 + q3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z6a−6 + z6a−8 + z6a−10 + 5z4a−6 + 2z4a−8 + 3z4a−10−z4a−12 + 8z2a−6−2z2a−8 + 3z2a−10−2z2a−12 + 4a−6−4a−8 + 2a−10−a−12

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−10 + z10a−12 + z9a−9 + 4z9a−11 + 3z9a−13 + z8a−8−3z8a−10 + z8a−12 + 5z8a−14 + z7a−7−z7a−9−13z7a−11−6z7a−13 + 5z7a−15 + z6a−6 + 11z6a−10−4z6a−12−13z6a−14 + 3z6a−16−2z5a−7 + 3z5a−9 + 25z5a−11 + 7z5a−13−12z5a−15 + z5a−17−5z4a−6−7z4a−8−15z4a−10 + 7z4a−12 + 14z4a−14−6z4a−16−2z3a−7−10z3a−9−20z3a−11−2z3a−13 + 8z3a−15−2z3a−17 + 8z2a−6 + 9z2a−8 + 6z2a−10−z2a−12−5z2a−14 + z2a−16 + 4za−7 + 6za−9 + 5za−11 + za−13−2za−15−4a−6−4a−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["K11a245"];

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]=

{ 3t3−9t2 + 16t−19 + 16t−1−9t−2 + 3t−3, −q14 + 3q13−6q12 + 9q11−11q10 + 12q9−12q8 + 9q7−6q6 + 4q5−q4 + 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]=

{10_66,}

In[6]:=

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

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

Out[6]=

{}