In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[8, 1]] |
Out[2]= | PD[X[1, 4, 2, 5], X[9, 12, 10, 13], X[3, 11, 4, 10], X[11, 3, 12, 2],
X[5, 16, 6, 1], X[7, 14, 8, 15], X[13, 8, 14, 9], X[15, 6, 16, 7]] |
In[3]:= | GaussCode[Knot[8, 1]] |
Out[3]= | GaussCode[-1, 4, -3, 1, -5, 8, -6, 7, -2, 3, -4, 2, -7, 6, -8, 5] |
In[4]:= | DTCode[Knot[8, 1]] |
Out[4]= | DTCode[4, 10, 16, 14, 12, 2, 8, 6] |
In[5]:= | br = BR[Knot[8, 1]] |
Out[5]= | BR[5, {-1, -1, -2, 1, -2, -3, 2, 4, -3, 4}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {5, 10} |
In[7]:= | BraidIndex[Knot[8, 1]] |
Out[7]= | 5 |
In[8]:= | Show[DrawMorseLink[Knot[8, 1]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[8, 1]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, 1, 1, 2, {4, 5}, 1} |
In[10]:= | alex = Alexander[Knot[8, 1]][t] |
Out[10]= | 3
7 - - - 3 t
t |
In[11]:= | Conway[Knot[8, 1]][z] |
Out[11]= | 2
1 - 3 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[8, 1]} |
In[13]:= | {KnotDet[Knot[8, 1]], KnotSignature[Knot[8, 1]]} |
Out[13]= | {13, 0} |
In[14]:= | Jones[Knot[8, 1]][q] |
Out[14]= | -6 -5 -4 2 2 2 2
2 + q - q + q - -- + -- - - - q + q
3 2 q
q q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[8, 1], Knot[11, NonAlternating, 70]} |
In[16]:= | A2Invariant[Knot[8, 1]][q] |
Out[16]= | -20 -18 -12 -10 2 6 8
q + q - q - q + q + q + q |
In[17]:= | HOMFLYPT[Knot[8, 1]][a, z] |
Out[17]= | -2 4 6 2 2 2 4 2
a - a + a - z - a z - a z |
In[18]:= | Kauffman[Knot[8, 1]][a, z] |
Out[18]= | 2 3
-2 4 6 3 5 z 4 2 6 2 z 3
-a - a - a - 3 a z - 3 a z + -- + 7 a z + 6 a z + -- - a z +
2 a
a
3 3 5 3 4 2 4 4 4 6 4 5
5 a z + 7 a z + z - 2 a z - 8 a z - 5 a z + a z -
3 5 5 5 2 6 4 6 6 6 3 7 5 7
4 a z - 5 a z + a z + 2 a z + a z + a z + a z |
In[19]:= | {Vassiliev[2][Knot[8, 1]], Vassiliev[3][Knot[8, 1]]} |
Out[19]= | {-3, 3} |
In[20]:= | Kh[Knot[8, 1]][q, t] |
Out[20]= | 1 1 1 1 1 1 1 1
- + 2 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- +
q 13 6 9 5 9 4 7 3 5 3 5 2 3 2
q t q t q t q t q t q t q t
1 1 5 2
---- + --- + q t + q t
3 q t
q t |
In[21]:= | ColouredJones[Knot[8, 1], 2][q] |
Out[21]= | -18 -17 -16 2 -14 2 3 3 3 3 3
2 + q - q - q + --- - q - --- + --- - --- + -- - -- + -- +
15 13 12 10 9 7 6
q q q q q q q
-5 3 2 -2 3 2 3 5 6
q - -- + -- + q - - - 2 q + 2 q - q + q
4 3 q
q q |