In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[9, 5]] |
Out[2]= | PD[X[6, 2, 7, 1], X[14, 6, 15, 5], X[18, 8, 1, 7], X[16, 10, 17, 9],
X[10, 16, 11, 15], X[8, 18, 9, 17], X[2, 14, 3, 13], X[12, 4, 13, 3],
X[4, 12, 5, 11]] |
In[3]:= | GaussCode[Knot[9, 5]] |
Out[3]= | GaussCode[1, -7, 8, -9, 2, -1, 3, -6, 4, -5, 9, -8, 7, -2, 5, -4, 6, -3] |
In[4]:= | DTCode[Knot[9, 5]] |
Out[4]= | DTCode[6, 12, 14, 18, 16, 4, 2, 10, 8] |
In[5]:= | br = BR[Knot[9, 5]] |
Out[5]= | BR[5, {1, 1, 2, -1, 2, 2, 3, -2, 3, 4, -3, 4}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {5, 12} |
In[7]:= | BraidIndex[Knot[9, 5]] |
Out[7]= | 5 |
In[8]:= | Show[DrawMorseLink[Knot[9, 5]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[9, 5]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, 2, 1, 2, {4, 6}, 1} |
In[10]:= | alex = Alexander[Knot[9, 5]][t] |
Out[10]= | 6
-11 + - + 6 t
t |
In[11]:= | Conway[Knot[9, 5]][z] |
Out[11]= | 2
1 + 6 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[9, 5]} |
In[13]:= | {KnotDet[Knot[9, 5]], KnotSignature[Knot[9, 5]]} |
Out[13]= | {23, 2} |
In[14]:= | Jones[Knot[9, 5]][q] |
Out[14]= | 2 3 4 5 6 7 8 9 10
q - 2 q + 3 q - 3 q + 4 q - 3 q + 3 q - 2 q + q - q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[9, 5]} |
In[16]:= | A2Invariant[Knot[9, 5]][q] |
Out[16]= | 2 4 8 12 14 16 18 22 26 30 32
q - q + q + q + q + q + q + q - q - q - q |
In[17]:= | HOMFLYPT[Knot[9, 5]][a, z] |
Out[17]= | 2 2 2 2
-10 -6 -4 z 2 z 2 z z
-a + a + a + -- + ---- + ---- + --
8 6 4 2
a a a a |
In[18]:= | Kauffman[Knot[9, 5]][a, z] |
Out[18]= | 2 2 2 2 2 3
-10 -6 -4 6 z 6 z 3 z 4 z 3 z 3 z z 11 z
a - a + a - --- - --- - ---- + ---- + ---- - ---- + -- + ----- +
11 9 10 8 6 4 2 11
a a a a a a a a
3 3 3 3 4 4 4 4 5 5
18 z z 4 z 2 z 7 z 3 z 7 z 3 z 6 z 14 z
----- + -- - ---- + ---- + ---- - ---- - ---- + ---- - ---- - ----- -
9 7 5 3 10 8 6 4 11 9
a a a a a a a a a a
5 5 6 6 6 7 7 7 8 8
5 z 3 z 5 z 2 z 3 z z 3 z 2 z z z
---- + ---- - ---- - ---- + ---- + --- + ---- + ---- + --- + --
7 5 10 8 6 11 9 7 10 8
a a a a a a a a a a |
In[19]:= | {Vassiliev[2][Knot[9, 5]], Vassiliev[3][Knot[9, 5]]} |
Out[19]= | {6, 15} |
In[20]:= | Kh[Knot[9, 5]][q, t] |
Out[20]= | 3 3 5 2 7 2 7 3 9 3 9 4
q + q + 2 q t + q t + 2 q t + 2 q t + q t + 2 q t +
11 4 11 5 13 5 13 6 15 6 17 7
2 q t + q t + 2 q t + 2 q t + q t + 2 q t +
17 8 21 9
q t + q t |
In[21]:= | ColouredJones[Knot[9, 5], 2][q] |
Out[21]= | 2 3 4 5 6 7 8 9 10 11
q - 2 q + q + 3 q - 5 q + 3 q + 3 q - 7 q + 5 q + 3 q -
12 13 14 15 16 17 18 19
8 q + 5 q + 5 q - 10 q + 4 q + 6 q - 9 q + 2 q +
20 21 23 24 25 26 27 28 29
6 q - 7 q + 5 q - 4 q - q + 3 q - q - q + q |