K11a355

K11a355 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["K11a355"];

In[4]:=

Alexander[K][t]

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

Out[4]=

2t4−4t3 + 6t2−7t + 7−7t−1 + 6t−2−4t−3 + 2t−4

In[5]:=

Conway[K][z]

Out[5]=

2z8 + 12z6 + 22z4 + 13z2 + 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]=

{ 45, 8 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q15 + 2q14−4q13 + 5q12−6q11 + 7q10−6q9 + 5q8−4q7 + 3q6−q5 + q4

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z8a−8 + z8a−10 + 7z6a−8 + 6z6a−10−z6a−12 + 16z4a−8 + 11z4a−10−5z4a−12 + 13z2a−8 + 7z2a−10−7z2a−12 + 2a−8 + 2a−10−3a−12

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−10 + z10a−12 + z9a−9 + 3z9a−11 + 2z9a−13 + z8a−8−5z8a−10−3z8a−12 + 3z8a−14−5z7a−9−14z7a−11−6z7a−13 + 3z7a−15−7z6a−8 + 8z6a−10 + 3z6a−12−9z6a−14 + 3z6a−16 + 6z5a−9 + 18z5a−11 + 4z5a−13−5z5a−15 + 3z5a−17 + 16z4a−8−8z4a−10−9z4a−12 + 10z4a−14−3z4a−16 + 2z4a−18−8z3a−11−2z3a−13 + 2z3a−15−3z3a−17 + z3a−19−13z2a−8 + 7z2a−10 + 11z2a−12−7z2a−14 + z2a−16−z2a−18−za−9 + 3za−11−za−15 + 2za−17−za−19 + 2a−8−2a−10−3a−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["K11a355"];

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]=

{ 2t4−4t3 + 6t2−7t + 7−7t−1 + 6t−2−4t−3 + 2t−4, −q15 + 2q14−4q13 + 5q12−6q11 + 7q10−6q9 + 5q8−4q7 + 3q6−q5 + q4 }

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]=

{}