K11a31

K11a31 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["K11a31"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−3t3 + 14t2−28t + 35−28t−1 + 14t−2−3t−3

In[5]:=

Conway[K][z]

Out[5]=

−3z6−4z4 + z2 + 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]=

{ 125, 4 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q11 + 4q10−8q9 + 13q8−18q7 + 20q6−20q5 + 17q4−12q3 + 8q2−3q + 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−z4a−4−7z4a−6 + 3z4a−8 + 2z2a−2 + 3z2a−4−10z2a−6 + 7z2a−8−z2a−10 + a−2 + 3a−4−6a−6 + 4a−8−a−10

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−6 + z10a−8 + 4z9a−5 + 8z9a−7 + 4z9a−9 + 5z8a−4 + 13z8a−6 + 15z8a−8 + 7z8a−10 + 3z7a−3−2z7a−5−4z7a−7 + 8z7a−9 + 7z7a−11 + z6a−2−11z6a−4−37z6a−6−35z6a−8−6z6a−10 + 4z6a−12−7z5a−3−10z5a−5−20z5a−7−29z5a−9−11z5a−11 + z5a−13−3z4a−2 + 8z4a−4 + 38z4a−6 + 30z4a−8−3z4a−10−6z4a−12 + 4z3a−3 + 10z3a−5 + 25z3a−7 + 26z3a−9 + 6z3a−11−z3a−13 + 3z2a−2−6z2a−4−22z2a−6−13z2a−8 + 2z2a−10 + 2z2a−12−4za−5−9za−7−7za−9−2za−11−a−2 + 3a−4 + 6a−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["K11a31"];

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 + 14t2−28t + 35−28t−1 + 14t−2−3t−3, −q11 + 4q10−8q9 + 13q8−18q7 + 20q6−20q5 + 17q4−12q3 + 8q2−3q + 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]=

{K11a317,}

In[6]:=

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

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

Out[6]=

{}