K11a259

K11a259 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["K11a259"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 5t3−10t2 + 15t−17 + 15t−1−10t−2 + 5t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−3z6 + 4z2 + 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]=

{ 79, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q12 + 3q11−6q10 + 9q9−11q8 + 12q7−12q6 + 10q5−7q4 + 5q3−2q2 + 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−4−13z4a−6 + 9z4a−8−z4a−10 + 8z2a−4−13z2a−6 + 12z2a−8−3z2a−10 + 4a−4−6a−6 + 5a−8−2a−10

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−6 + z10a−8 + 2z9a−5 + 6z9a−7 + 4z9a−9 + z8a−4 + z8a−6 + 8z8a−8 + 8z8a−10−10z7a−5−22z7a−7−2z7a−9 + 10z7a−11−6z6a−4−22z6a−6−42z6a−8−17z6a−10 + 9z6a−12 + 15z5a−5 + 17z5a−7−24z5a−9−20z5a−11 + 6z5a−13 + 13z4a−4 + 44z4a−6 + 53z4a−8 + 6z4a−10−13z4a−12 + 3z4a−14−5z3a−5 + 6z3a−7 + 26z3a−9 + 10z3a−11−4z3a−13 + z3a−15−12z2a−4−28z2a−6−25z2a−8−4z2a−10 + 5z2a−12−2za−5−5za−7−7za−9−3za−11 + za−13 + 4a−4 + 6a−6 + 5a−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["K11a259"];

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 + 5t3−10t2 + 15t−17 + 15t−1−10t−2 + 5t−3−t−4, −q12 + 3q11−6q10 + 9q9−11q8 + 12q7−12q6 + 10q5−7q4 + 5q3−2q2 + 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]=

{K11a221,}

In[6]:=

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

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

Out[6]=

{}