10 83

2009-05-22T18:59:16Z

DartrOcrel:

http://www.textletoacelouli.com



{{Rolfsen Knot Page|
n = 10 |
k = 83 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-5,6,-2,1,-4,5,-6,7,-8,9,-3,4,-10,2,-9,8,-7,3/goTop.html |
braid_table = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width = 4 |
braid_index = 4 |
same_alexander = [[K11a307]], [[K11a323]], |
same_jones = [[10_73]], |
khovanov_table = <table border=1>
<tr align=center>
<td width=13.3333%><table cellpadding=0 cellspacing=0>
<tr><td>\</td><td> </td><td>r</td></tr>
<tr><td> </td><td> \ </td><td> </td></tr>
<tr><td>j</td><td> </td><td>\</td></tr>
</table></td>
<td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=6.66667%>5</td ><td width=6.66667%>6</td ><td width=6.66667%>7</td ><td width=13.3333%>χ</td></tr>
<tr align=center><td>17</td><td> </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>
<tr align=center><td>15</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td>2</td></tr>
<tr align=center><td>13</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td> </td><td>-3</td></tr>
<tr align=center><td>11</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td>-3</td></tr>
<tr align=center><td>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>6</td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>5</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>3</td><td> </td><td> </td><td> </td><td bgcolor=yellow>5</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>1</td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-1</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>
<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-5</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> </td><td>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{23}-3 q^{22}+2 q^{21}+7 q^{20}-18 q^{19}+7 q^{18}+32 q^{17}-52 q^{16}+q^{15}+85 q^{14}-91 q^{13}-26 q^{12}+145 q^{11}-110 q^{10}-61 q^9+175 q^8-97 q^7-83 q^6+159 q^5-59 q^4-82 q^3+107 q^2-19 q-56+48 q^{-1} + q^{-2} -23 q^{-3} +12 q^{-4} +2 q^{-5} -4 q^{-6} + q^{-7} </math> |
coloured_jones_3 = <math>-q^{45}+3 q^{44}-2 q^{43}-3 q^{42}+2 q^{41}+11 q^{40}-9 q^{39}-24 q^{38}+17 q^{37}+54 q^{36}-25 q^{35}-105 q^{34}+16 q^{33}+184 q^{32}+20 q^{31}-279 q^{30}-97 q^{29}+372 q^{28}+226 q^{27}-457 q^{26}-378 q^{25}+498 q^{24}+555 q^{23}-507 q^{22}-725 q^{21}+481 q^{20}+867 q^{19}-422 q^{18}-972 q^{17}+339 q^{16}+1036 q^{15}-243 q^{14}-1047 q^{13}+129 q^{12}+1015 q^{11}-18 q^{10}-925 q^9-100 q^8+806 q^7+184 q^6-640 q^5-251 q^4+481 q^3+255 q^2-308 q-243+186 q^{-1} +186 q^{-2} -88 q^{-3} -132 q^{-4} +39 q^{-5} +76 q^{-6} -8 q^{-7} -45 q^{-8} +4 q^{-9} +19 q^{-10} -7 q^{-12} -2 q^{-13} +4 q^{-14} - q^{-15} </math> |
coloured_jones_4 = <math>q^{74}-3 q^{73}+2 q^{72}+3 q^{71}-6 q^{70}+5 q^{69}-10 q^{68}+15 q^{67}+14 q^{66}-41 q^{65}+4 q^{64}-23 q^{63}+81 q^{62}+83 q^{61}-145 q^{60}-91 q^{59}-127 q^{58}+270 q^{57}+411 q^{56}-196 q^{55}-390 q^{54}-670 q^{53}+370 q^{52}+1205 q^{51}+313 q^{50}-577 q^{49}-1952 q^{48}-303 q^{47}+2055 q^{46}+1750 q^{45}+188 q^{44}-3487 q^{43}-2140 q^{42}+2023 q^{41}+3557 q^{40}+2245 q^{39}-4266 q^{38}-4474 q^{37}+760 q^{36}+4730 q^{35}+4842 q^{34}-3919 q^{33}-6263 q^{32}-1085 q^{31}+4893 q^{30}+6944 q^{29}-2870 q^{28}-7048 q^{27}-2771 q^{26}+4292 q^{25}+8120 q^{24}-1549 q^{23}-6895 q^{22}-4044 q^{21}+3122 q^{20}+8329 q^{19}-40 q^{18}-5817 q^{17}-4833 q^{16}+1397 q^{15}+7463 q^{14}+1463 q^{13}-3823 q^{12}-4793 q^{11}-530 q^{10}+5457 q^9+2331 q^8-1433 q^7-3648 q^6-1787 q^5+2909 q^4+2051 q^3+296 q^2-1883 q-1794+940 q^{-1} +1045 q^{-2} +770 q^{-3} -530 q^{-4} -1028 q^{-5} +117 q^{-6} +245 q^{-7} +472 q^{-8} -19 q^{-9} -371 q^{-10} -3 q^{-11} -13 q^{-12} +160 q^{-13} +30 q^{-14} -101 q^{-15} +10 q^{-16} -20 q^{-17} +38 q^{-18} +10 q^{-19} -24 q^{-20} +4 q^{-21} -5 q^{-22} +7 q^{-23} +2 q^{-24} -4 q^{-25} + q^{-26} </math> |
coloured_jones_5 = |
coloured_jones_6 = |
coloured_jones_7 = |
computer_talk =
<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=    </pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 83]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[1, 6, 2, 7], X[5, 16, 6, 17], X[13, 1, 14, 20], X[7, 15, 8, 14],

X[3, 9, 4, 8], X[9, 5, 10, 4], X[19, 11, 20, 10], X[11, 19, 12, 18],

X[17, 13, 18, 12], X[15, 2, 16, 3]]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[10, 83]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[-1, 10, -5, 6, -2, 1, -4, 5, -6, 7, -8, 9, -3, 4, -10, 2, -9,

8, -7, 3]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 83]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 16, 14, 4, 18, 20, 2, 12, 10]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 83]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td>
<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, -3, 2, 2, -3, 2, -3}]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
<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>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
<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>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 83]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 83]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_83_ML.gif]]</td></tr><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 83]]&) /@ {
SymmetryType, UnknottingNumber, ThreeGenus,
BridgeIndex, SuperBridgeIndex, NakanishiIndex
}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Chiral, 2, 3, 3, NotAvailable, 1}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 83]][t]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 9 19 2 3
-23 + -- - -- + -- + 19 t - 9 t + 2 t
3 2 t
t t</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 83]][z]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6
1 + z + 3 z + 2 z</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td>
<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>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 83], Knot[11, Alternating, 307], Knot[11, Alternating, 323]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 83]], KnotSignature[Knot[10, 83]]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{83, 2}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 83]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -2 4 2 3 4 5 6 7 8
-7 - q + - + 11 q - 13 q + 14 q - 13 q + 10 q - 6 q + 3 q - q
q</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<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>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 73], Knot[10, 83]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 83]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -6 2 2 4 6 8 12 14 16 18
-q + -- + 3 q - 3 q + 2 q - q + 2 q - 2 q + 3 q - q -
4
q

20 22 24
q + q - q</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 83]][a, z]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 4 4 4 6 6
-6 2 -2 2 2 z 4 z 4 z 3 z 2 z z z
1 - a + -- - a - z - ---- + ---- - z - -- + ---- + ---- + -- + --
4 6 4 6 4 2 4 2
a a a a a a a a</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 83]][a, z]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 2
-6 2 -2 3 z 6 z 4 z z 2 2 z 4 z 10 z
1 + a + -- + a - --- - --- - --- - - + 2 z + ---- - ---- - ----- -
4 7 5 3 a 8 6 4
a a a a a a a

2 3 3 3 3 3 4
2 z 2 z 9 z 20 z 13 z 3 z 3 4 6 z
---- - ---- + ---- + ----- + ----- + ---- - a z - 7 z - ---- +
2 9 7 5 3 a 8
a a a a a a

4 4 4 5 5 5 5 5
10 z 22 z z z 11 z 18 z 17 z 10 z 5
----- + ----- - -- + -- - ----- - ----- - ----- - ----- + a z +
6 4 2 9 7 5 3 a
a a a a a a a

6 6 6 6 7 7 7 7
6 3 z 10 z 22 z 5 z 5 z 5 z 6 z 6 z
4 z + ---- - ----- - ----- - ---- + ---- + ---- + ---- + ---- +
8 6 4 2 7 5 3 a
a a a a a a a

8 8 8 9 9
5 z 10 z 5 z 2 z 2 z
---- + ----- + ---- + ---- + ----
6 4 2 5 3
a a a a a</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 83]], Vassiliev[3][Knot[10, 83]]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{1, 2}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 83]][q, t]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 3 1 4 3 q 3 5
7 q + 5 q + ----- + ----- + ---- + --- + --- + 7 q t + 6 q t +
5 3 3 2 2 q t t
q t q t q t

5 2 7 2 7 3 9 3 9 4 11 4
7 q t + 7 q t + 6 q t + 7 q t + 4 q t + 6 q t +

11 5 13 5 13 6 15 6 17 7
2 q t + 4 q t + q t + 2 q t + q t</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 83], 2][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -7 4 2 12 23 -2 48 2 3
-56 + q - -- + -- + -- - -- + q + -- - 19 q + 107 q - 82 q -
6 5 4 3 q
q q q q

4 5 6 7 8 9 10 11
59 q + 159 q - 83 q - 97 q + 175 q - 61 q - 110 q + 145 q -

12 13 14 15 16 17 18 19
26 q - 91 q + 85 q + q - 52 q + 32 q + 7 q - 18 q +

20 21 22 23
7 q + 2 q - 3 q + q</nowiki></code></td></tr>
</table> }}

Knot Atlas - User contributions [en]

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