9 10: Difference between revisions
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<tr><td>j</td><td> </td><td>\</td></tr> |
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<td width=7.14286%>0</td ><td width=7.14286%>1</td ><td width=7.14286%>2</td ><td width=7.14286%>3</td ><td width=7.14286%>4</td ><td width=7.14286%>5</td ><td width=7.14286%>6</td ><td width=7.14286%>7</td ><td width=7.14286%>8</td ><td width=7.14286%>9</td ><td width=14.2857%>χ</td></tr> |
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<tr align=center><td>23</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td>-1</td></tr> |
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<tr align=center><td>21</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td>0</td></tr> |
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<tr align=center><td>19</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td> </td><td>-2</td></tr> |
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<tr align=center><td>17</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td> </td><td> </td><td>2</td></tr> |
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<tr align=center><td>15</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td>0</td></tr> |
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<tr align=center><td>13</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr> |
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<tr align=center><td>11</td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr> |
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<tr align=center><td>9</td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr> |
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<tr align=center><td>7</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr> |
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<tr align=center><td>5</td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr> |
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<tr align=center><td>3</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr> |
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</table> | |
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coloured_jones_2 = <math>q^{31}-q^{30}+3 q^{28}-4 q^{27}-2 q^{26}+10 q^{25}-10 q^{24}-7 q^{23}+22 q^{22}-14 q^{21}-15 q^{20}+32 q^{19}-13 q^{18}-22 q^{17}+35 q^{16}-11 q^{15}-22 q^{14}+28 q^{13}-5 q^{12}-16 q^{11}+15 q^{10}-8 q^8+5 q^7+q^6-2 q^5+q^4</math> | |
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coloured_jones_3 = <math>-q^{60}+q^{59}-2 q^{56}+3 q^{55}-q^{53}-5 q^{52}+8 q^{51}+5 q^{50}-7 q^{49}-16 q^{48}+16 q^{47}+21 q^{46}-13 q^{45}-37 q^{44}+13 q^{43}+50 q^{42}-10 q^{41}-62 q^{40}-q^{39}+76 q^{38}+7 q^{37}-81 q^{36}-22 q^{35}+94 q^{34}+24 q^{33}-90 q^{32}-37 q^{31}+94 q^{30}+36 q^{29}-84 q^{28}-43 q^{27}+77 q^{26}+41 q^{25}-60 q^{24}-41 q^{23}+46 q^{22}+35 q^{21}-28 q^{20}-32 q^{19}+19 q^{18}+21 q^{17}-6 q^{16}-17 q^{15}+4 q^{14}+9 q^{13}-6 q^{11}+q^{10}+2 q^9+q^8-2 q^7+q^6</math> | |
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coloured_jones_4 = <math>q^{98}-q^{97}-q^{94}+3 q^{93}-3 q^{92}+q^{91}+2 q^{90}-5 q^{89}+6 q^{88}-8 q^{87}+2 q^{86}+9 q^{85}-6 q^{84}+11 q^{83}-25 q^{82}-5 q^{81}+21 q^{80}+7 q^{79}+34 q^{78}-55 q^{77}-35 q^{76}+20 q^{75}+28 q^{74}+97 q^{73}-72 q^{72}-83 q^{71}-22 q^{70}+27 q^{69}+193 q^{68}-49 q^{67}-122 q^{66}-94 q^{65}-14 q^{64}+284 q^{63}+8 q^{62}-125 q^{61}-172 q^{60}-79 q^{59}+349 q^{58}+69 q^{57}-107 q^{56}-232 q^{55}-137 q^{54}+379 q^{53}+114 q^{52}-80 q^{51}-261 q^{50}-180 q^{49}+373 q^{48}+138 q^{47}-44 q^{46}-252 q^{45}-204 q^{44}+318 q^{43}+139 q^{42}+5 q^{41}-203 q^{40}-203 q^{39}+220 q^{38}+108 q^{37}+50 q^{36}-120 q^{35}-168 q^{34}+113 q^{33}+55 q^{32}+66 q^{31}-43 q^{30}-108 q^{29}+44 q^{28}+8 q^{27}+48 q^{26}-2 q^{25}-51 q^{24}+16 q^{23}-10 q^{22}+23 q^{21}+5 q^{20}-20 q^{19}+8 q^{18}-7 q^{17}+8 q^{16}+3 q^{15}-7 q^{14}+3 q^{13}-2 q^{12}+2 q^{11}+q^{10}-2 q^9+q^8</math> | |
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coloured_jones_5 = | |
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coloured_jones_6 = | |
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coloured_jones_7 = | |
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computer_talk = |
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<table> |
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<tr valign=top> |
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:= </pre></td> |
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<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
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</tr> |
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<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[9, 10]]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[8, 2, 9, 1], X[12, 4, 13, 3], X[18, 10, 1, 9], X[10, 18, 11, 17], |
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X[16, 8, 17, 7], X[2, 12, 3, 11], X[4, 16, 5, 15], X[14, 6, 15, 5], |
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X[6, 14, 7, 13]]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[9, 10]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -6, 2, -7, 8, -9, 5, -1, 3, -4, 6, -2, 9, -8, 7, -5, 4, -3]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[9, 10]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[8, 12, 14, 16, 18, 2, 6, 4, 10]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[9, 10]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[4, {1, 1, 2, -1, 2, 2, 2, 2, 3, -2, 3}]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{4, 11}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[9, 10]]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[9, 10]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:9_10_ML.gif]]</td></tr><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[9, 10]]&) /@ { |
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SymmetryType, UnknottingNumber, ThreeGenus, |
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BridgeIndex, SuperBridgeIndex, NakanishiIndex |
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}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, {2, 3}, 2, 2, {4, 6}, 1}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[9, 10]][t]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 4 8 2 |
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9 + -- - - - 8 t + 4 t |
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2 t |
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t</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[9, 10]][z]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 |
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1 + 8 z + 4 z</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[9, 10]}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[9, 10]], KnotSignature[Knot[9, 10]]}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{33, 4}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[9, 10]][q]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 3 4 5 6 7 8 9 10 11 |
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q - 2 q + 4 q - 5 q + 6 q - 5 q + 5 q - 3 q + q - q</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[9, 10]}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[9, 10]][q]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 6 8 10 16 20 22 24 26 28 30 32 |
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q - q + q + 2 q + 2 q + q + q + q - 2 q - q - q - |
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34 |
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q</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[9, 10]][a, z]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 2 2 4 4 4 |
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-2 -8 2 z 2 z 5 z 2 z z 2 z z |
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--- + a + -- - --- + ---- + ---- + ---- + -- + ---- + -- |
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10 6 10 8 6 4 8 6 4 |
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a a a a a a a a a</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[9, 10]][a, z]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 2 2 3 3 |
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2 -8 2 4 z 4 z 11 z 2 z 7 z 2 z 4 z z |
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--- + a - -- + --- - --- - ----- - ---- + ---- - ---- - ---- - --- + |
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10 6 13 9 10 8 6 4 13 11 |
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a a a a a a a a a a |
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3 3 3 4 4 4 4 4 5 5 |
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9 z 3 z 3 z 2 z 9 z 3 z 7 z z z z |
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---- + ---- - ---- - ---- + ---- + ---- - ---- + -- + --- - --- - |
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9 7 5 12 10 8 6 4 13 11 |
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a a a a a a a a a a |
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5 5 5 6 6 6 6 7 7 7 |
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7 z 3 z 2 z z 3 z z 3 z z 3 z 2 z |
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---- - ---- + ---- + --- - ---- - -- + ---- + --- + ---- + ---- + |
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9 7 5 12 10 8 6 11 9 7 |
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a a a a a a a a a a |
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8 8 |
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z z |
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--- + -- |
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10 8 |
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a a</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[9, 10]], Vassiliev[3][Knot[9, 10]]}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{8, 22}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[9, 10]][q, t]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 5 5 7 2 9 2 9 3 11 3 11 4 |
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q + q + 2 q t + 2 q t + 2 q t + 3 q t + 2 q t + 3 q t + |
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13 4 13 5 15 5 15 6 17 6 19 7 |
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3 q t + 2 q t + 3 q t + 3 q t + 2 q t + 3 q t + |
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19 8 23 9 |
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q t + q t</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[9, 10], 2][q]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 4 5 6 7 8 10 11 12 13 |
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q - 2 q + q + 5 q - 8 q + 15 q - 16 q - 5 q + 28 q - |
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14 15 16 17 18 19 20 |
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22 q - 11 q + 35 q - 22 q - 13 q + 32 q - 15 q - |
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21 22 23 24 25 26 27 28 |
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14 q + 22 q - 7 q - 10 q + 10 q - 2 q - 4 q + 3 q - |
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30 31 |
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q + q</nowiki></code></td></tr> |
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</table> }} |
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Revision as of 18:30, 10 April 2007
{{Rolfsen Knot Page| n = 9 | k = 10 | KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-7,8,-9,5,-1,3,-4,6,-2,9,-8,7,-5,4,-3/goTop.html |
braid_table =
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braid_crossings = 11 | braid_width = 4 | braid_index = 4 | same_alexander = | same_jones = |
khovanov_table =
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