K11a42

K11a42 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["K11a42"];

In[4]:=

Alexander[K][t]

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

Out[4]=

t3−9t2 + 26t−35 + 26t−1−9t−2 + t−3

In[5]:=

Conway[K][z]

Out[5]=

z6−3z4−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]=

{ 107, 2 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q8 + 3q7−6q6 + 11q5−15q4 + 17q3−17q2 + 15q−11 + 7q−1−3q−2 + q−3

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z6a−2 + 2z4a−2−3z4a−4−2z4 + a2z2 + 3z2a−2−5z2a−4 + 3z2a−6−3z2 + a2 + 2a−2−3a−4 + 3a−6−a−8−1

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z10a−2 + z10a−4 + 3z9a−1 + 6z9a−3 + 3z9a−5 + 7z8a−2 + 7z8a−4 + 4z8a−6 + 4z8 + 3az7−5z7a−3 + 2z7a−5 + 4z7a−7 + a2z6−15z6a−2−10z6a−4 + 3z6a−8−7z6−8az5−11z5a−1−5z5a−3−7z5a−5−4z5a−7 + z5a−9−3a2z4 + 4z4a−2−2z4a−4−10z4a−6−6z4a−8−z4 + 6az3 + 7z3a−1 + 5z3a−3 + 5z3a−5−z3a−7−2z3a−9 + 3a2z2 + 3z2a−2 + 9z2a−4 + 11z2a−6 + 4z2a−8 + 4z2−az−za−1−za−3−za−5 + za−7 + za−9−a2−2a−2−3a−4−3a−6−a−8−1

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["K11a42"];

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]=

{ t3−9t2 + 26t−35 + 26t−1−9t−2 + t−3, −q8 + 3q7−6q6 + 11q5−15q4 + 17q3−17q2 + 15q−11 + 7q−1−3q−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]=

{}

In[6]:=

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

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

Out[6]=

{K11a10,}