In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[8, 4]] |
Out[2]= | PD[X[6, 2, 7, 1], X[14, 10, 15, 9], X[10, 3, 11, 4], X[2, 13, 3, 14],
X[12, 5, 13, 6], X[16, 8, 1, 7], X[4, 11, 5, 12], X[8, 16, 9, 15]] |
In[3]:= | GaussCode[Knot[8, 4]] |
Out[3]= | GaussCode[1, -4, 3, -7, 5, -1, 6, -8, 2, -3, 7, -5, 4, -2, 8, -6] |
In[4]:= | DTCode[Knot[8, 4]] |
Out[4]= | DTCode[6, 10, 12, 16, 14, 4, 2, 8] |
In[5]:= | br = BR[Knot[8, 4]] |
Out[5]= | BR[4, {-1, -1, -1, 2, -1, 2, 3, -2, 3}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {4, 9} |
In[7]:= | BraidIndex[Knot[8, 4]] |
Out[7]= | 4 |
In[8]:= | Show[DrawMorseLink[Knot[8, 4]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[8, 4]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, 2, 2, 2, {3, 5}, 1} |
In[10]:= | alex = Alexander[Knot[8, 4]][t] |
Out[10]= | 2 5 2
-5 - -- + - + 5 t - 2 t
2 t
t |
In[11]:= | Conway[Knot[8, 4]][z] |
Out[11]= | 2 4
1 - 3 z - 2 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[8, 4]} |
In[13]:= | {KnotDet[Knot[8, 4]], KnotSignature[Knot[8, 4]]} |
Out[13]= | {19, -2} |
In[14]:= | Jones[Knot[8, 4]][q] |
Out[14]= | -5 2 3 3 3 2 3
-3 + q - -- + -- - -- + - + 2 q - q + q
4 3 2 q
q q q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[8, 4]} |
In[16]:= | A2Invariant[Knot[8, 4]][q] |
Out[16]= | -16 -10 -6 -4 -2 2 4 6 8 10
-1 + q + q + q - q - q - q + q + q + q + q |
In[17]:= | HOMFLYPT[Knot[8, 4]][a, z] |
Out[17]= | 2
2 4 2 z 2 2 4 2 4 2 4
-2 + -- + a - 3 z + -- - 2 a z + a z - z - a z
2 2
a a |
In[18]:= | Kauffman[Knot[8, 4]][a, z] |
Out[18]= | 2
2 4 z 3 2 7 z 2 2 4 2
-2 - -- + a - - + a z + 2 a z + 10 z + ---- - a z - 3 a z +
2 a 2
a a
3 4
6 2 4 z 3 3 3 5 3 4 5 z 2 4
a z + ---- - 3 a z - 5 a z + 2 a z - 11 z - ---- - 3 a z +
a 2
a
5 6 7
4 4 4 z 5 3 5 6 z 2 6 z 7
3 a z - ---- - a z + 3 a z + 3 z + -- + 2 a z + -- + a z
a 2 a
a |
In[19]:= | {Vassiliev[2][Knot[8, 4]], Vassiliev[3][Knot[8, 4]]} |
Out[19]= | {-3, 1} |
In[20]:= | Kh[Knot[8, 4]][q, t] |
Out[20]= | 2 2 1 1 1 2 1 1 2 2 t
-- + - + ------ + ----- + ----- + ----- + ----- + ---- + ---- + --- +
3 q 11 4 9 3 7 3 7 2 5 2 5 3 q
q q t q t q t q t q t q t q t
3 2 3 3 7 4
q t + 2 q t + q t + q t |
In[21]:= | ColouredJones[Knot[8, 4], 2][q] |
Out[21]= | -14 2 -12 3 6 3 4 9 5 5 10 4
2 + q - --- + q + --- - --- + -- + -- - -- + -- + -- - -- + -- +
13 11 10 9 8 7 6 5 4 3
q q q q q q q q q q
7 9 2 4 5 6 7 8 9 10
-- - - + 7 q - 7 q + 5 q - 4 q - q + 3 q - q - q + q
2 q
q |