K11a25

K11a25 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["K11a25"];

In[4]:=

Alexander[K][t]

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

Out[4]=

−t4 + 6t3−18t2 + 33t−39 + 33t−1−18t−2 + 6t−3−t−4

In[5]:=

Conway[K][z]

Out[5]=

−z8−2z6−2z4−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]=

{ 155, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q8 + 4q7−9q6 + 16q5−22q4 + 25q3−25q2 + 22q−16 + 10q−1−4q−2 + q−3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

−z8a−2−5z6a−2 + 2z6a−4 + z6−11z4a−2 + 7z4a−4−z4a−6 + 3z4−12z2a−2 + 9z2a−4−2z2a−6 + 4z2−5a−2 + 4a−4−a−6 + 3

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

2z10a−2 + 2z10a−4 + 7z9a−1 + 14z9a−3 + 7z9a−5 + 19z8a−2 + 21z8a−4 + 10z8a−6 + 8z8 + 4az7−6z7a−1−14z7a−3 + 4z7a−5 + 8z7a−7 + a2z6−55z6a−2−52z6a−4−12z6a−6 + 4z6a−8−18z6−8az5−11z5a−1−17z5a−3−26z5a−5−11z5a−7 + z5a−9−2a2z4 + 50z4a−2 + 43z4a−4 + 5z4a−6−5z4a−8 + 15z4 + 5az3 + 11z3a−1 + 21z3a−3 + 23z3a−5 + 7z3a−7−z3a−9 + a2z2−24z2a−2−18z2a−4−z2a−6 + 2z2a−8−8z2−az−3za−1−6za−3−6za−5−2za−7 + 5a−2 + 4a−4 + a−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["K11a25"];

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 + 6t3−18t2 + 33t−39 + 33t−1−18t−2 + 6t−3−t−4, −q8 + 4q7−9q6 + 16q5−22q4 + 25q3−25q2 + 22q−16 + 10q−1−4q−2 + q−3 }

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]=

{K11a19, K11a281,}

In[6]:=

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

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

Out[6]=

{K11a19,}