10 58: Difference between revisions
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<td width=6.66667%>-6</td ><td width=6.66667%>-5</td ><td width=6.66667%>-4</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=13.3333%>χ</td></tr> |
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<tr align=center><td>9</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> |
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<tr align=center><td>7</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 bgcolor=yellow> </td><td>-1</td></tr> |
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<tr align=center><td>5</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> |
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<tr align=center><td>3</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> </td><td>-3</td></tr> |
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<tr align=center><td>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td>2</td></tr> |
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<tr align=center><td>-1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr> |
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<tr align=center><td>-3</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr> |
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<tr align=center><td>-5</td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>6</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>-7</td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</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>-9</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> |
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<tr align=center><td>-11</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> </td><td> </td><td>-2</td></tr> |
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<tr align=center><td>-13</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> |
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</table> | |
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coloured_jones_2 = <math>q^{12}-2 q^{11}+q^{10}+4 q^9-10 q^8+7 q^7+12 q^6-32 q^5+20 q^4+30 q^3-66 q^2+29 q+57-91 q^{-1} +23 q^{-2} +76 q^{-3} -91 q^{-4} +6 q^{-5} +78 q^{-6} -68 q^{-7} -12 q^{-8} +63 q^{-9} -36 q^{-10} -20 q^{-11} +36 q^{-12} -10 q^{-13} -13 q^{-14} +11 q^{-15} -3 q^{-17} + q^{-18} </math> | |
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coloured_jones_3 = <math>q^{24}-2 q^{23}+q^{22}+2 q^{20}-5 q^{19}+4 q^{18}+2 q^{17}-5 q^{16}-8 q^{15}+22 q^{14}+5 q^{13}-37 q^{12}-21 q^{11}+80 q^{10}+33 q^9-120 q^8-72 q^7+171 q^6+125 q^5-215 q^4-190 q^3+242 q^2+259 q-247-320 q^{-1} +229 q^{-2} +370 q^{-3} -198 q^{-4} -393 q^{-5} +146 q^{-6} +403 q^{-7} -92 q^{-8} -392 q^{-9} +31 q^{-10} +366 q^{-11} +31 q^{-12} -328 q^{-13} -81 q^{-14} +269 q^{-15} +130 q^{-16} -210 q^{-17} -151 q^{-18} +138 q^{-19} +157 q^{-20} -77 q^{-21} -136 q^{-22} +22 q^{-23} +109 q^{-24} +5 q^{-25} -69 q^{-26} -20 q^{-27} +38 q^{-28} +20 q^{-29} -17 q^{-30} -13 q^{-31} +6 q^{-32} +5 q^{-33} -3 q^{-35} + q^{-36} </math> | |
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coloured_jones_4 = <math>q^{40}-2 q^{39}+q^{38}-2 q^{36}+7 q^{35}-8 q^{34}+4 q^{33}-q^{32}-11 q^{31}+25 q^{30}-15 q^{29}+11 q^{28}-15 q^{27}-45 q^{26}+73 q^{25}+10 q^{24}+36 q^{23}-85 q^{22}-173 q^{21}+155 q^{20}+152 q^{19}+179 q^{18}-229 q^{17}-550 q^{16}+148 q^{15}+464 q^{14}+639 q^{13}-300 q^{12}-1234 q^{11}-182 q^{10}+755 q^9+1456 q^8-29 q^7-1959 q^6-867 q^5+712 q^4+2296 q^3+600 q^2-2318 q-1568+273 q^{-1} +2743 q^{-2} +1280 q^{-3} -2192 q^{-4} -1939 q^{-5} -311 q^{-6} +2691 q^{-7} +1722 q^{-8} -1742 q^{-9} -1928 q^{-10} -840 q^{-11} +2279 q^{-12} +1905 q^{-13} -1119 q^{-14} -1659 q^{-15} -1274 q^{-16} +1629 q^{-17} +1873 q^{-18} -392 q^{-19} -1172 q^{-20} -1561 q^{-21} +812 q^{-22} +1571 q^{-23} +276 q^{-24} -490 q^{-25} -1520 q^{-26} +26 q^{-27} +963 q^{-28} +608 q^{-29} +188 q^{-30} -1071 q^{-31} -412 q^{-32} +277 q^{-33} +482 q^{-34} +529 q^{-35} -456 q^{-36} -383 q^{-37} -135 q^{-38} +148 q^{-39} +446 q^{-40} -56 q^{-41} -143 q^{-42} -175 q^{-43} -53 q^{-44} +198 q^{-45} +41 q^{-46} +5 q^{-47} -71 q^{-48} -62 q^{-49} +47 q^{-50} +15 q^{-51} +20 q^{-52} -10 q^{-53} -20 q^{-54} +6 q^{-55} +5 q^{-57} -3 q^{-59} + q^{-60} </math> | |
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coloured_jones_5 = <math>q^{60}-2 q^{59}+q^{58}-2 q^{56}+3 q^{55}+4 q^{54}-8 q^{53}+q^{52}+3 q^{51}-8 q^{50}+10 q^{49}+14 q^{48}-21 q^{47}-9 q^{46}+3 q^{45}-4 q^{44}+36 q^{43}+41 q^{42}-47 q^{41}-82 q^{40}-45 q^{39}+34 q^{38}+184 q^{37}+181 q^{36}-96 q^{35}-365 q^{34}-366 q^{33}+36 q^{32}+668 q^{31}+826 q^{30}+63 q^{29}-1048 q^{28}-1507 q^{27}-542 q^{26}+1488 q^{25}+2637 q^{24}+1327 q^{23}-1766 q^{22}-4006 q^{21}-2804 q^{20}+1707 q^{19}+5681 q^{18}+4795 q^{17}-1109 q^{16}-7200 q^{15}-7358 q^{14}-202 q^{13}+8431 q^{12}+10157 q^{11}+2142 q^{10}-9044 q^9-12831 q^8-4599 q^7+8938 q^6+15092 q^5+7226 q^4-8168 q^3-16662 q^2-9688 q+6860+17481 q^{-1} +11752 q^{-2} -5299 q^{-3} -17577 q^{-4} -13272 q^{-5} +3673 q^{-6} +17126 q^{-7} +14227 q^{-8} -2146 q^{-9} -16230 q^{-10} -14734 q^{-11} +700 q^{-12} +15120 q^{-13} +14863 q^{-14} +628 q^{-15} -13722 q^{-16} -14762 q^{-17} -1986 q^{-18} +12146 q^{-19} +14447 q^{-20} +3341 q^{-21} -10288 q^{-22} -13866 q^{-23} -4733 q^{-24} +8135 q^{-25} +12989 q^{-26} +6033 q^{-27} -5764 q^{-28} -11665 q^{-29} -7050 q^{-30} +3187 q^{-31} +9899 q^{-32} +7679 q^{-33} -758 q^{-34} -7696 q^{-35} -7632 q^{-36} -1427 q^{-37} +5246 q^{-38} +6977 q^{-39} +2970 q^{-40} -2803 q^{-41} -5663 q^{-42} -3832 q^{-43} +685 q^{-44} +4017 q^{-45} +3853 q^{-46} +893 q^{-47} -2264 q^{-48} -3300 q^{-49} -1753 q^{-50} +801 q^{-51} +2302 q^{-52} +1953 q^{-53} +287 q^{-54} -1310 q^{-55} -1672 q^{-56} -786 q^{-57} +446 q^{-58} +1126 q^{-59} +915 q^{-60} +86 q^{-61} -609 q^{-62} -727 q^{-63} -322 q^{-64} +209 q^{-65} +458 q^{-66} +340 q^{-67} +19 q^{-68} -233 q^{-69} -253 q^{-70} -84 q^{-71} +80 q^{-72} +132 q^{-73} +95 q^{-74} -6 q^{-75} -71 q^{-76} -55 q^{-77} -4 q^{-78} +15 q^{-79} +24 q^{-80} +20 q^{-81} -10 q^{-82} -13 q^{-83} - q^{-84} +5 q^{-87} -3 q^{-89} + q^{-90} </math> | |
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coloured_jones_6 = <math>q^{84}-2 q^{83}+q^{82}-2 q^{80}+3 q^{79}+4 q^{77}-11 q^{76}+5 q^{75}+6 q^{74}-13 q^{73}+9 q^{72}+4 q^{71}+8 q^{70}-35 q^{69}+14 q^{68}+33 q^{67}-31 q^{66}+14 q^{65}+8 q^{64}-7 q^{63}-104 q^{62}+35 q^{61}+134 q^{60}+q^{59}+56 q^{58}-24 q^{57}-166 q^{56}-376 q^{55}+11 q^{54}+473 q^{53}+386 q^{52}+433 q^{51}-56 q^{50}-866 q^{49}-1518 q^{48}-590 q^{47}+1143 q^{46}+1977 q^{45}+2404 q^{44}+770 q^{43}-2440 q^{42}-5191 q^{41}-3931 q^{40}+896 q^{39}+5519 q^{38}+8774 q^{37}+5840 q^{36}-3087 q^{35}-12736 q^{34}-14275 q^{33}-5126 q^{32}+8535 q^{31}+21464 q^{30}+20913 q^{29}+3711 q^{28}-20763 q^{27}-33790 q^{26}-23968 q^{25}+2797 q^{24}+35737 q^{23}+47742 q^{22}+25842 q^{21}-19296 q^{20}-55795 q^{19}-56250 q^{18}-19856 q^{17}+39828 q^{16}+77149 q^{15}+62162 q^{14}-176 q^{13}-66747 q^{12}-90348 q^{11}-56332 q^{10}+25849 q^9+94225 q^8+98984 q^7+31972 q^6-59204 q^5-110932 q^4-91890 q^3-565 q^2+92403 q+121569+62685 q^{-1} -39334 q^{-2} -112917 q^{-3} -113494 q^{-4} -26119 q^{-5} +78166 q^{-6} +126576 q^{-7} +81477 q^{-8} -18714 q^{-9} -102975 q^{-10} -119790 q^{-11} -43052 q^{-12} +61269 q^{-13} +120653 q^{-14} +88906 q^{-15} -2616 q^{-16} -89116 q^{-17} -117304 q^{-18} -53331 q^{-19} +44956 q^{-20} +110170 q^{-21} +91149 q^{-22} +11750 q^{-23} -72997 q^{-24} -110909 q^{-25} -62305 q^{-26} +26139 q^{-27} +95418 q^{-28} +91347 q^{-29} +28507 q^{-30} -51354 q^{-31} -99432 q^{-32} -71019 q^{-33} +2037 q^{-34} +72749 q^{-35} +86347 q^{-36} +46392 q^{-37} -22402 q^{-38} -78314 q^{-39} -73965 q^{-40} -23928 q^{-41} +40923 q^{-42} +70135 q^{-43} +57488 q^{-44} +8709 q^{-45} -46453 q^{-46} -63587 q^{-47} -41731 q^{-48} +6538 q^{-49} +41592 q^{-50} +52988 q^{-51} +30341 q^{-52} -11733 q^{-53} -39075 q^{-54} -41933 q^{-55} -17472 q^{-56} +9876 q^{-57} +32877 q^{-58} +33080 q^{-59} +12006 q^{-60} -10965 q^{-61} -25847 q^{-62} -22234 q^{-63} -10742 q^{-64} +9074 q^{-65} +19913 q^{-66} +16939 q^{-67} +6488 q^{-68} -6498 q^{-69} -12371 q^{-70} -14007 q^{-71} -4760 q^{-72} +4437 q^{-73} +9148 q^{-74} +8804 q^{-75} +3734 q^{-76} -1233 q^{-77} -7148 q^{-78} -5993 q^{-79} -2838 q^{-80} +1026 q^{-81} +3675 q^{-82} +4012 q^{-83} +3001 q^{-84} -1002 q^{-85} -2170 q^{-86} -2599 q^{-87} -1575 q^{-88} -153 q^{-89} +1214 q^{-90} +2087 q^{-91} +732 q^{-92} +179 q^{-93} -683 q^{-94} -878 q^{-95} -809 q^{-96} -167 q^{-97} +595 q^{-98} +350 q^{-99} +416 q^{-100} +81 q^{-101} -106 q^{-102} -346 q^{-103} -228 q^{-104} +62 q^{-105} +12 q^{-106} +132 q^{-107} +86 q^{-108} +59 q^{-109} -71 q^{-110} -66 q^{-111} +3 q^{-112} -27 q^{-113} +15 q^{-114} +15 q^{-115} +29 q^{-116} -10 q^{-117} -13 q^{-118} +6 q^{-119} -7 q^{-120} +5 q^{-123} -3 q^{-125} + q^{-126} </math> | |
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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[10, 58]]</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[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[1, 4, 2, 5], X[7, 10, 8, 11], X[3, 9, 4, 8], X[9, 3, 10, 2], |
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X[5, 14, 6, 15], X[11, 19, 12, 18], X[15, 20, 16, 1], |
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X[19, 16, 20, 17], X[17, 13, 18, 12], X[13, 6, 14, 7]]</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[10, 58]]</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, 4, -3, 1, -5, 10, -2, 3, -4, 2, -6, 9, -10, 5, -7, 8, -9, |
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6, -8, 7]</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[10, 58]]</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[4, 8, 14, 10, 2, 18, 6, 20, 12, 16]</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[10, 58]]</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[6, {1, -2, 1, 3, -2, -4, -3, -3, 5, -4, 5}]</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>{6, 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[10, 58]]</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>6</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[10, 58]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:10_58_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[10, 58]]&) /@ { |
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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, 2, 3, NotAvailable, 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[10, 58]][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> 3 16 2 |
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27 + -- - -- - 16 t + 3 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[10, 58]][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 - 4 z + 3 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[10, 58]}</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[10, 58]], KnotSignature[Knot[10, 58]]}</nowiki></code></td></tr> |
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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>{65, 0}</nowiki></code></td></tr> |
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</table> |
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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[10, 58]][q]</nowiki></code></td></tr> |
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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> -6 3 6 8 10 11 2 3 4 |
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10 + q - -- + -- - -- + -- - -- - 8 q + 5 q - 2 q + q |
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5 4 3 2 q |
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q q q q</nowiki></code></td></tr> |
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</table> |
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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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<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[10, 58]}</nowiki></code></td></tr> |
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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[10, 58]][q]</nowiki></code></td></tr> |
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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> -20 -18 2 -14 2 3 -4 2 4 6 |
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-2 + q + q - --- + q - --- + -- + q + q - 3 q + q + |
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16 10 8 |
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q q q |
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8 10 12 14 |
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2 q - q + q + q</nowiki></code></td></tr> |
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</table> |
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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[10, 58]][a, z]</nowiki></code></td></tr> |
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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 |
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-4 2 4 6 2 2 z 2 2 4 2 4 |
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-2 + a + 3 a - 2 a + a - 2 z - ---- + 3 a z - 3 a z + z + |
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2 |
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a |
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2 4 |
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2 a z</nowiki></code></td></tr> |
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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[10, 58]][a, z]</nowiki></code></td></tr> |
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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> -4 2 4 6 4 z 3 5 2 |
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-2 + a - 3 a - 2 a - a - --- - 6 a z - 4 a z - 2 a z + 8 z - |
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a |
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2 3 3 |
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2 z 2 2 4 2 6 2 2 z 8 z 3 |
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---- + 10 a z + 7 a z + 3 a z - ---- + ---- + 21 a z + |
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4 3 a |
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a a |
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4 4 |
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3 3 5 3 4 z 2 z 2 4 4 4 6 4 |
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18 a z + 7 a z - 5 z + -- - ---- - 4 a z - 5 a z - 3 a z + |
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4 2 |
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a a |
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5 5 6 |
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2 z 6 z 5 3 5 5 5 6 3 z 2 6 |
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---- - ---- - 22 a z - 23 a z - 9 a z - z + ---- - 10 a z - |
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3 a 2 |
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a a |
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7 |
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4 6 6 6 4 z 7 3 7 5 7 8 |
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5 a z + a z + ---- + 7 a z + 6 a z + 3 a z + 3 z + |
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a |
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2 8 4 8 9 3 9 |
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6 a z + 3 a z + a z + a z</nowiki></code></td></tr> |
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</table> |
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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[10, 58]], Vassiliev[3][Knot[10, 58]]}</nowiki></code></td></tr> |
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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>{-4, 1}</nowiki></code></td></tr> |
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</table> |
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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[10, 58]][q, t]</nowiki></code></td></tr> |
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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>5 1 2 1 4 2 4 4 |
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- + 6 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- + |
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q 13 6 11 5 9 5 9 4 7 4 7 3 5 3 |
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q t q t q t q t q t q t q t |
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6 4 5 6 3 3 2 5 2 |
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----- + ----- + ---- + --- + 4 q t + 4 q t + q t + 4 q t + |
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5 2 3 2 3 q t |
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q t q t q t |
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5 3 7 3 9 4 |
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q t + q t + q t</nowiki></code></td></tr> |
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</table> |
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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[10, 58], 2][q]</nowiki></code></td></tr> |
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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> -18 3 11 13 10 36 20 36 63 12 68 |
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57 + q - --- + --- - --- - --- + --- - --- - --- + -- - -- - -- + |
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17 15 14 13 12 11 10 9 8 7 |
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q q q q q q q q q q |
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78 6 91 76 23 91 2 3 4 5 |
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-- + -- - -- + -- + -- - -- + 29 q - 66 q + 30 q + 20 q - 32 q + |
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6 5 4 3 2 q |
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q q q q q |
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6 7 8 9 10 11 12 |
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12 q + 7 q - 10 q + 4 q + q - 2 q + q</nowiki></code></td></tr> |
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</table> }} |
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Revision as of 09:44, 7 June 2007
{{Rolfsen Knot Page| n = 10 | k = 58 | KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,10,-2,3,-4,2,-6,9,-10,5,-7,8,-9,6,-8,7/goTop.html |
braid_table =
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braid_crossings = 11 | braid_width = 6 | braid_index = 6 | same_alexander = | same_jones = |
khovanov_table =
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