K11a20

K11a20 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["K11a20"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−3t3 + 13t2−25t + 31−25t−1 + 13t−2−3t−3

In[5]:=

Conway[K][z]

Out[5]=

−3z6−5z4 + 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]=

{ 113, 4 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q11 + 4q10−8q9 + 13q8−17q7 + 18q6−18q5 + 15q4−10q3 + 6q2−2q + 1

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

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

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−6 + z10a−8 + 3z9a−5 + 7z9a−7 + 4z9a−9 + 3z8a−4 + 8z8a−6 + 12z8a−8 + 7z8a−10 + 2z7a−3−4z7a−5−8z7a−7 + 5z7a−9 + 7z7a−11 + z6a−2−6z6a−4−26z6a−6−30z6a−8−7z6a−10 + 4z6a−12−5z5a−3 + z5a−5−5z5a−7−23z5a−9−11z5a−11 + z5a−13−4z4a−2 + 3z4a−4 + 34z4a−6 + 30z4a−8−3z4a−10−6z4a−12 + 2z3a−3 + 14z3a−7 + 22z3a−9 + 5z3a−11−z3a−13 + 5z2a−2−2z2a−4−22z2a−6−15z2a−8 + 2z2a−10 + 2z2a−12 + za−3−za−5−7za−7−7za−9−2za−11−2a−2 + a−4 + 5a−6 + 4a−8 + a−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["K11a20"];

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 + 13t2−25t + 31−25t−1 + 13t−2−3t−3, −q11 + 4q10−8q9 + 13q8−17q7 + 18q6−18q5 + 15q4−10q3 + 6q2−2q + 1 }

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]=

{}