In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[10, 86]] |
Out[2]= | PD[X[6, 2, 7, 1], X[16, 8, 17, 7], X[8, 3, 9, 4], X[2, 15, 3, 16],
X[14, 5, 15, 6], X[4, 9, 5, 10], X[20, 14, 1, 13], X[10, 20, 11, 19],
X[18, 12, 19, 11], X[12, 18, 13, 17]] |
In[3]:= | GaussCode[Knot[10, 86]] |
Out[3]= | GaussCode[1, -4, 3, -6, 5, -1, 2, -3, 6, -8, 9, -10, 7, -5, 4, -2, 10,
-9, 8, -7] |
In[4]:= | DTCode[Knot[10, 86]] |
Out[4]= | DTCode[6, 8, 14, 16, 4, 18, 20, 2, 12, 10] |
In[5]:= | br = BR[Knot[10, 86]] |
Out[5]= | BR[4, {-1, -1, 2, -1, 2, -1, 2, 2, 3, -2, 3}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {4, 11} |
In[7]:= | BraidIndex[Knot[10, 86]] |
Out[7]= | 4 |
In[8]:= | Show[DrawMorseLink[Knot[10, 86]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[10, 86]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Chiral, 2, 3, 3, NotAvailable, 1} |
In[10]:= | alex = Alexander[Knot[10, 86]][t] |
Out[10]= | 2 9 19 2 3
25 - -- + -- - -- - 19 t + 9 t - 2 t
3 2 t
t t |
In[11]:= | Conway[Knot[10, 86]][z] |
Out[11]= | 2 4 6
1 - z - 3 z - 2 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[10, 86], Knot[11, Alternating, 190]} |
In[13]:= | {KnotDet[Knot[10, 86]], KnotSignature[Knot[10, 86]]} |
Out[13]= | {85, 0} |
In[14]:= | Jones[Knot[10, 86]][q] |
Out[14]= | -4 4 8 11 2 3 4 5 6
14 + q - -- + -- - -- - 14 q + 13 q - 10 q + 6 q - 3 q + q
3 2 q
q q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[10, 60], Knot[10, 86]} |
In[16]:= | A2Invariant[Knot[10, 86]][q] |
Out[16]= | -12 2 -8 -6 2 4 2 6 8 10
-1 + q - --- + q + q - -- + -- + 2 q - 2 q + 2 q - 3 q +
10 4 2
q q q
12 14 16 18
q + q - q + q |
In[17]:= | HOMFLYPT[Knot[10, 86]][a, z] |
Out[17]= | 2 2 4 4 6
-4 2 2 z 4 z 2 2 4 z 3 z 2 4 6 z
2 + a - -- + ---- - ---- + a z - 2 z + -- - ---- + a z - z - --
2 4 2 4 2 2
a a a a a a |
In[18]:= | Kauffman[Knot[10, 86]][a, z] |
Out[18]= | 2 2 2
-4 2 2 z 4 z 3 z 2 2 z 2 z 6 z
2 + a + -- - --- - --- - --- - a z + z + ---- - ---- - ---- +
2 5 3 a 6 4 2
a a a a a a
3 3 3 4
2 2 8 z 15 z 13 z 3 3 3 4 3 z
3 a z + ---- + ----- + ----- + 4 a z - 2 a z - 7 z - ---- +
5 3 a 6
a a a
4 4 5 5 5
7 z 13 z 2 4 4 4 9 z 17 z 23 z 5
---- + ----- - 9 a z + a z - ---- - ----- - ----- - 11 a z +
4 2 5 3 a
a a a a
6 6 6 7 7 7
3 5 6 z 10 z 21 z 2 6 3 z 3 z 9 z
4 a z - 2 z + -- - ----- - ----- + 8 a z + ---- + ---- + ---- +
6 4 2 5 3 a
a a a a a
8 8 9 9
7 8 4 z 10 z 2 z 2 z
9 a z + 6 z + ---- + ----- + ---- + ----
4 2 3 a
a a a |
In[19]:= | {Vassiliev[2][Knot[10, 86]], Vassiliev[3][Knot[10, 86]]} |
Out[19]= | {-1, -1} |
In[20]:= | Kh[Knot[10, 86]][q, t] |
Out[20]= | 8 1 3 1 5 3 6 5
- + 7 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 7 q t +
q 9 4 7 3 5 3 5 2 3 2 3 q t
q t q t q t q t q t q t
3 3 2 5 2 5 3 7 3 7 4 9 4
7 q t + 6 q t + 7 q t + 4 q t + 6 q t + 2 q t + 4 q t +
9 5 11 5 13 6
q t + 2 q t + q t |
In[21]:= | ColouredJones[Knot[10, 86], 2][q] |
Out[21]= | -12 4 4 9 27 16 37 77 28 88 133 22
140 + q - --- + --- + -- - -- + -- + -- - -- + -- + -- - --- + -- -
11 10 9 8 7 6 5 4 3 2 q
q q q q q q q q q q
2 3 4 5 6 7 8
159 q - 2 q + 163 q - 140 q - 30 q + 146 q - 90 q - 45 q +
9 10 11 12 13 14 15 16
97 q - 36 q - 37 q + 43 q - 5 q - 17 q + 10 q + q -
17 18
3 q + q |