In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[10, 47]] |
Out[2]= | PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[9, 17, 10, 16], X[5, 15, 6, 14],
X[15, 7, 16, 6], X[11, 19, 12, 18], X[13, 1, 14, 20],
X[17, 11, 18, 10], X[19, 13, 20, 12], X[7, 2, 8, 3]] |
In[3]:= | GaussCode[Knot[10, 47]] |
Out[3]= | GaussCode[-1, 10, -2, 1, -4, 5, -10, 2, -3, 8, -6, 9, -7, 4, -5, 3, -8,
6, -9, 7] |
In[4]:= | DTCode[Knot[10, 47]] |
Out[4]= | DTCode[4, 8, 14, 2, 16, 18, 20, 6, 10, 12] |
In[5]:= | br = BR[Knot[10, 47]] |
Out[5]= | BR[3, {1, 1, 1, 1, 1, -2, 1, 1, -2, -2}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {3, 10} |
In[7]:= | BraidIndex[Knot[10, 47]] |
Out[7]= | 3 |
In[8]:= | Show[DrawMorseLink[Knot[10, 47]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[10, 47]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, {2, 3}, 4, 3, NotAvailable, 1} |
In[10]:= | alex = Alexander[Knot[10, 47]][t] |
Out[10]= | -4 3 6 7 2 3 4
7 + t - -- + -- - - - 7 t + 6 t - 3 t + t
3 2 t
t t |
In[11]:= | Conway[Knot[10, 47]][z] |
Out[11]= | 2 4 6 8
1 + 6 z + 8 z + 5 z + z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[10, 47]} |
In[13]:= | {KnotDet[Knot[10, 47]], KnotSignature[Knot[10, 47]]} |
Out[13]= | {41, 4} |
In[14]:= | Jones[Knot[10, 47]][q] |
Out[14]= | 1 2 3 4 5 6 7 8 9
2 - - - 3 q + 5 q - 5 q + 7 q - 6 q + 5 q - 4 q + 2 q - q
q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[10, 47]} |
In[16]:= | A2Invariant[Knot[10, 47]][q] |
Out[16]= | -2 2 6 8 10 12 14 18 20 22 26
-q - q + q + q + 4 q + q + 3 q - q - q - 2 q - q |
In[17]:= | HOMFLYPT[Knot[10, 47]][a, z] |
Out[17]= | 2 2 2 4 4 4 6 6
-5 9 3 8 z 21 z 7 z 5 z 18 z 5 z z 7 z
-- + -- - -- - ---- + ----- - ---- - ---- + ----- - ---- - -- + ---- -
6 4 2 6 4 2 6 4 2 6 4
a a a a a a a a a a a
6 8
z z
-- + --
2 4
a a |
In[18]:= | Kauffman[Knot[10, 47]][a, z] |
Out[18]= | 2 2 2
5 9 3 z 2 z z 9 z 8 z 3 z z z 15 z
-- + -- + -- - --- + --- - -- - --- - --- - --- - --- + -- - ----- -
6 4 2 11 9 7 5 3 a 10 8 6
a a a a a a a a a a a
2 2 3 3 3 3 3 3 4
26 z 9 z z 3 z 2 z 19 z 20 z 7 z 2 z
----- - ---- + --- - ---- + ---- + ----- + ----- + ---- + ---- -
4 2 11 9 7 5 3 a 10
a a a a a a a a
4 4 4 4 5 5 5 5 5
3 z 15 z 35 z 15 z 3 z 5 z 14 z 11 z 5 z
---- + ----- + ----- + ----- + ---- - ---- - ----- - ----- - ---- +
8 6 4 2 9 7 5 3 a
a a a a a a a a
6 6 6 6 7 7 7 7 8 8
3 z 10 z 23 z 10 z 3 z z z z 3 z 5 z
---- - ----- - ----- - ----- + ---- + -- - -- + -- + ---- + ---- +
8 6 4 2 7 5 3 a 6 4
a a a a a a a a a
8 9 9
2 z z z
---- + -- + --
2 5 3
a a a |
In[19]:= | {Vassiliev[2][Knot[10, 47]], Vassiliev[3][Knot[10, 47]]} |
Out[19]= | {6, 11} |
In[20]:= | Kh[Knot[10, 47]][q, t] |
Out[20]= | 3
3 5 1 1 q 2 q q 5 7
3 q + 3 q + ----- + ---- + -- + --- + -- + 3 q t + 2 q t +
3 3 2 2 t t
q t q t t
7 2 9 2 9 3 11 3 11 4 13 4
4 q t + 3 q t + 2 q t + 4 q t + 3 q t + 2 q t +
13 5 15 5 15 6 17 6 19 7
q t + 3 q t + q t + q t + q t |
In[21]:= | ColouredJones[Knot[10, 47], 2][q] |
Out[21]= | -5 2 -3 6 5 2 3 4 5
-6 + q - -- - q + -- - - + 14 q - 4 q - 15 q + 19 q + q -
4 2 q
q q
6 7 8 9 10 11 12 13
22 q + 20 q + 7 q - 26 q + 17 q + 11 q - 25 q + 11 q +
14 15 16 17 18 19 20 21
12 q - 20 q + 8 q + 7 q - 13 q + 7 q + 2 q - 7 q +
22 23 24 25
4 q + q - 2 q + q |