K11a9

K11a9 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["K11a9"];

In[4]:=

Alexander[K][t]

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

Out[4]=

t4−5t3 + 10t2−11t + 11−11t−1 + 10t−2−5t−3 + t−4

In[5]:=

Conway[K][z]

Out[5]=

z8 + 3z6 + 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]=

{ 65, 4 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q9 + 3q8−5q7 + 7q6−9q5 + 10q4−9q3 + 8q2−6q + 4−2q−1 + q−2

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z8a−4−2z6a−2 + 6z6a−4−z6a−6−10z4a−2 + 13z4a−4−4z4a−6 + z4−14z2a−2 + 14z2a−4−4z2a−6 + 4z2−6a−2 + 6a−4−2a−6 + 3

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−2 + z10a−4 + 2z9a−1 + 6z9a−3 + 4z9a−5 + 5z8a−4 + 6z8a−6 + z8−11z7a−1−28z7a−3−11z7a−5 + 6z7a−7−20z6a−2−36z6a−4−16z6a−6 + 6z6a−8−6z6 + 19z5a−1 + 38z5a−3 + 5z5a−5−9z5a−7 + 5z5a−9 + 44z4a−2 + 54z4a−4 + 12z4a−6−7z4a−8 + 3z4a−10 + 12z4−12z3a−1−17z3a−3−z3a−5−z3a−7−4z3a−9 + z3a−11−30z2a−2−29z2a−4−7z2a−6 + z2a−8−z2a−10−10z2 + 2za−1 + 3za−3 + za−5 + za−7 + za−9 + 6a−2 + 6a−4 + 2a−6 + 3

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["K11a9"];

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 + 10t2−11t + 11−11t−1 + 10t−2−5t−3 + t−4, −q9 + 3q8−5q7 + 7q6−9q5 + 10q4−9q3 + 8q2−6q + 4−2q−1 + q−2 }

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]=

{K11a140,}