In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[9, 46]] |
Out[2]= | PD[X[4, 2, 5, 1], X[7, 12, 8, 13], X[10, 3, 11, 4], X[2, 11, 3, 12],
X[5, 14, 6, 15], X[13, 6, 14, 7], X[15, 18, 16, 1], X[9, 17, 10, 16],
X[17, 9, 18, 8]] |
In[3]:= | GaussCode[Knot[9, 46]] |
Out[3]= | GaussCode[1, -4, 3, -1, -5, 6, -2, 9, -8, -3, 4, 2, -6, 5, -7, 8, -9, 7] |
In[4]:= | DTCode[Knot[9, 46]] |
Out[4]= | DTCode[4, 10, -14, -12, -16, 2, -6, -18, -8] |
In[5]:= | br = BR[Knot[9, 46]] |
Out[5]= | BR[4, {-1, 2, -1, 2, -3, -2, 1, -2, -3}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {4, 9} |
In[7]:= | BraidIndex[Knot[9, 46]] |
Out[7]= | 4 |
In[8]:= | Show[DrawMorseLink[Knot[9, 46]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[9, 46]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, 2, 1, 3, 4, 2} |
In[10]:= | alex = Alexander[Knot[9, 46]][t] |
Out[10]= | 2
5 - - - 2 t
t |
In[11]:= | Conway[Knot[9, 46]][z] |
Out[11]= | 2
1 - 2 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[6, 1], Knot[9, 46], Knot[11, NonAlternating, 67],
Knot[11, NonAlternating, 97], Knot[11, NonAlternating, 139]} |
In[13]:= | {KnotDet[Knot[9, 46]], KnotSignature[Knot[9, 46]]} |
Out[13]= | {9, 0} |
In[14]:= | Jones[Knot[9, 46]][q] |
Out[14]= | -6 -5 -4 2 -2 1
2 + q - q + q - -- + q - -
3 q
q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[9, 46]} |
In[16]:= | A2Invariant[Knot[9, 46]][q] |
Out[16]= | -20 -18 -12 -10 -8 -6 -2 2
2 + q + q - q - q - q - q + q + 2 q |
In[17]:= | HOMFLYPT[Knot[9, 46]][a, z] |
Out[17]= | 2 4 6 2 2 4 2
2 - a - a + a - a z - a z |
In[18]:= | Kauffman[Knot[9, 46]][a, z] |
Out[18]= | 2 4 6 3 5 2 2 4 2
2 + a - a - a - 2 a z - 6 a z - 4 a z + 3 a z + 9 a z +
6 2 3 3 3 5 3 2 4 4 4 6 4
6 a z + a z + 8 a z + 7 a z - 4 a z - 9 a z - 5 a z -
3 5 5 5 2 6 4 6 6 6 3 7 5 7
5 a z - 5 a z + a z + 2 a z + a z + a z + a z |
In[19]:= | {Vassiliev[2][Knot[9, 46]], Vassiliev[3][Knot[9, 46]]} |
Out[19]= | {-2, 3} |
In[20]:= | Kh[Knot[9, 46]][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 3 2 3
q t q t q t q t q t q t q t |
In[21]:= | ColouredJones[Knot[9, 46], 2][q] |
Out[21]= | -18 -17 -16 2 -14 2 2 -10 2 2 1 2
q - q - q + --- - q - --- + --- - q + -- - -- + - + q
15 13 12 9 3 q
q q q q q |