K11n13

K11n13 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["K11n13"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 3t3−2t2 + t−1 + t−1−2t−2 + 3t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−5z6−4z4 + 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]=

{ 15, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q10 + q9−q8 + 2q7−2q6 + 2q5−2q4 + 2q3−q2 + q

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z8a−6 + z6a−4−7z6a−6 + z6a−8 + 6z4a−4−16z4a−6 + 6z4a−8 + 10z2a−4−15z2a−6 + 10z2a−8−z2a−10 + 4a−4−6a−6 + 5a−8−2a−10

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z9a−5 + z9a−7 + z8a−4 + 3z8a−6 + 2z8a−8−6z7a−5−5z7a−7 + z7a−9−7z6a−4−19z6a−6−12z6a−8 + 10z5a−5 + 6z5a−7−4z5a−9 + 16z4a−4 + 37z4a−6 + 23z4a−8 + 2z4a−10−4z3a−5−2z3a−7 + 3z3a−9 + z3a−11−14z2a−4−26z2a−6−19z2a−8−6z2a−10 + z2a−12 + za−7−za−9−za−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["K11n13"];

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 + 3t3−2t2 + t−1 + t−1−2t−2 + 3t−3−t−4, −q10 + q9−q8 + 2q7−2q6 + 2q5−2q4 + 2q3−q2 + 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]=

{9_2,}