K11a308

K11a308 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["K11a308"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 5t3−9t2 + 13t−15 + 13t−1−9t−2 + 5t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−3z6 + z4 + 6z2 + 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]=

{ 71, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q12 + 3q11−6q10 + 8q9−10q8 + 11q7−10q6 + 9q5−6q4 + 4q3−2q2 + q

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z8a−6 + z6a−4−6z6a−6 + 2z6a−8 + 5z4a−4−12z4a−6 + 9z4a−8−z4a−10 + 7z2a−4−9z2a−6 + 11z2a−8−3z2a−10 + 2a−4−2a−6 + 3a−8−2a−10

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−6 + z10a−8 + 2z9a−5 + 5z9a−7 + 3z9a−9 + z8a−4−z8a−6 + 4z8a−8 + 6z8a−10−11z7a−5−20z7a−7−z7a−9 + 8z7a−11−6z6a−4−12z6a−6−25z6a−8−11z6a−10 + 8z6a−12 + 19z5a−5 + 21z5a−7−18z5a−9−14z5a−11 + 6z5a−13 + 12z4a−4 + 26z4a−6 + 30z4a−8 + 2z4a−10−11z4a−12 + 3z4a−14−10z3a−5−4z3a−7 + 17z3a−9 + 5z3a−11−5z3a−13 + z3a−15−9z2a−4−14z2a−6−13z2a−8−4z2a−10 + 4z2a−12−4za−9−2za−11 + 2za−13 + 2a−4 + 2a−6 + 3a−8 + 2a−10

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["K11a308"];

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 + 5t3−9t2 + 13t−15 + 13t−1−9t−2 + 5t−3−t−4, −q12 + 3q11−6q10 + 8q9−10q8 + 11q7−10q6 + 9q5−6q4 + 4q3−2q2 + q }

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]=

{}