View source for 9 40

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{{Rolfsen Knot Page|
n = 9 |
k = 40 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-6,7,-3,1,-2,8,-7,5,-4,2,-9,3,-5,6,-8,9/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 9 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  = [[10_59]], [[K11n66]],  |
same_jones      =  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=14.2857%><table cellpadding=0 cellspacing=0>
  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
  <td width=7.14286%>-6</td    ><td width=7.14286%>-5</td    ><td width=7.14286%>-4</td    ><td width=7.14286%>-3</td    ><td width=7.14286%>-2</td    ><td width=7.14286%>-1</td    ><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=14.2857%>&chi;</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>&nbsp;</td><td>4</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-11</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr>
<tr align=center><td>-13</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-15</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^7-5 q^6+3 q^5+19 q^4-31 q^3-11 q^2+72 q-55-56 q^{-1} +133 q^{-2} -55 q^{-3} -109 q^{-4} +166 q^{-5} -34 q^{-6} -140 q^{-7} +157 q^{-8} -5 q^{-9} -132 q^{-10} +107 q^{-11} +17 q^{-12} -84 q^{-13} +45 q^{-14} +17 q^{-15} -29 q^{-16} +9 q^{-17} +4 q^{-18} -4 q^{-19} + q^{-20} </math> |
coloured_jones_3 = <math>-q^{15}+5 q^{14}-3 q^{13}-14 q^{12}+q^{11}+40 q^{10}+25 q^9-94 q^8-73 q^7+126 q^6+194 q^5-151 q^4-342 q^3+107 q^2+525 q-11-680 q^{-1} -158 q^{-2} +815 q^{-3} +344 q^{-4} -886 q^{-5} -544 q^{-6} +910 q^{-7} +728 q^{-8} -891 q^{-9} -880 q^{-10} +834 q^{-11} +994 q^{-12} -743 q^{-13} -1066 q^{-14} +620 q^{-15} +1083 q^{-16} -461 q^{-17} -1048 q^{-18} +293 q^{-19} +942 q^{-20} -124 q^{-21} -781 q^{-22} -12 q^{-23} +584 q^{-24} +96 q^{-25} -390 q^{-26} -115 q^{-27} +219 q^{-28} +98 q^{-29} -104 q^{-30} -63 q^{-31} +46 q^{-32} +25 q^{-33} -15 q^{-34} -9 q^{-35} +5 q^{-36} +4 q^{-37} -4 q^{-38} + q^{-39} </math> |
coloured_jones_4 = <math>q^{26}-5 q^{25}+3 q^{24}+14 q^{23}-6 q^{22}-10 q^{21}-54 q^{20}+12 q^{19}+123 q^{18}+63 q^{17}-8 q^{16}-354 q^{15}-217 q^{14}+329 q^{13}+537 q^{12}+505 q^{11}-830 q^{10}-1224 q^9-159 q^8+1186 q^7+2280 q^6-369 q^5-2607 q^4-2214 q^3+613 q^2+4687 q+1940-2721 q^{-1} -5063 q^{-2} -2006 q^{-3} +5964 q^{-4} +5176 q^{-5} -819 q^{-6} -6995 q^{-7} -5605 q^{-8} +5407 q^{-9} +7709 q^{-10} +2089 q^{-11} -7392 q^{-12} -8642 q^{-13} +3786 q^{-14} +8945 q^{-15} +4753 q^{-16} -6752 q^{-17} -10527 q^{-18} +1879 q^{-19} +9105 q^{-20} +6778 q^{-21} -5423 q^{-22} -11264 q^{-23} -219 q^{-24} +8166 q^{-25} +8099 q^{-26} -3234 q^{-27} -10564 q^{-28} -2414 q^{-29} +5814 q^{-30} +8187 q^{-31} -421 q^{-32} -8024 q^{-33} -3786 q^{-34} +2497 q^{-35} +6394 q^{-36} +1712 q^{-37} -4297 q^{-38} -3362 q^{-39} -139 q^{-40} +3403 q^{-41} +1991 q^{-42} -1284 q^{-43} -1701 q^{-44} -889 q^{-45} +1049 q^{-46} +1029 q^{-47} -90 q^{-48} -412 q^{-49} -473 q^{-50} +155 q^{-51} +259 q^{-52} +22 q^{-53} -21 q^{-54} -108 q^{-55} +17 q^{-56} +36 q^{-57} -7 q^{-58} +5 q^{-59} -13 q^{-60} +5 q^{-61} +4 q^{-62} -4 q^{-63} + q^{-64} </math> |
coloured_jones_5 = <math>-q^{40}+5 q^{39}-3 q^{38}-14 q^{37}+6 q^{36}+15 q^{35}+24 q^{34}+17 q^{33}-41 q^{32}-128 q^{31}-82 q^{30}+108 q^{29}+305 q^{28}+339 q^{27}-15 q^{26}-625 q^{25}-1030 q^{24}-470 q^{23}+913 q^{22}+2087 q^{21}+1848 q^{20}-388 q^{19}-3473 q^{18}-4496 q^{17}-1434 q^{16}+4095 q^{15}+7952 q^{14}+5796 q^{13}-2816 q^{12}-11610 q^{11}-12207 q^{10}-1714 q^9+13297 q^8+20201 q^7+10114 q^6-11699 q^5-27556 q^4-21711 q^3+5201 q^2+32487 q+34873+5850 q^{-1} -32966 q^{-2} -47451 q^{-3} -20537 q^{-4} +28725 q^{-5} +57365 q^{-6} +36598 q^{-7} -19905 q^{-8} -63518 q^{-9} -52284 q^{-10} +8290 q^{-11} +65649 q^{-12} +65809 q^{-13} +4624 q^{-14} -64378 q^{-15} -76575 q^{-16} -17251 q^{-17} +60870 q^{-18} +84414 q^{-19} +28638 q^{-20} -56107 q^{-21} -89768 q^{-22} -38508 q^{-23} +50814 q^{-24} +93288 q^{-25} +46955 q^{-26} -45264 q^{-27} -95300 q^{-28} -54407 q^{-29} +39130 q^{-30} +95958 q^{-31} +61317 q^{-32} -32026 q^{-33} -94929 q^{-34} -67633 q^{-35} +23316 q^{-36} +91462 q^{-37} +73166 q^{-38} -12823 q^{-39} -84934 q^{-40} -76887 q^{-41} +945 q^{-42} +74637 q^{-43} +77742 q^{-44} +11310 q^{-45} -60878 q^{-46} -74559 q^{-47} -22256 q^{-48} +44655 q^{-49} +66904 q^{-50} +30045 q^{-51} -27849 q^{-52} -55278 q^{-53} -33418 q^{-54} +12728 q^{-55} +41431 q^{-56} +31974 q^{-57} -1343 q^{-58} -27371 q^{-59} -26773 q^{-60} -5474 q^{-61} +15448 q^{-62} +19647 q^{-63} +7818 q^{-64} -6869 q^{-65} -12469 q^{-66} -7184 q^{-67} +1841 q^{-68} +6816 q^{-69} +5164 q^{-70} +254 q^{-71} -3096 q^{-72} -2986 q^{-73} -787 q^{-74} +1131 q^{-75} +1491 q^{-76} +578 q^{-77} -346 q^{-78} -588 q^{-79} -290 q^{-80} +65 q^{-81} +196 q^{-82} +134 q^{-83} -21 q^{-84} -75 q^{-85} -18 q^{-86} +7 q^{-87} +4 q^{-88} +13 q^{-89} + q^{-90} -13 q^{-91} +5 q^{-92} +4 q^{-93} -4 q^{-94} + q^{-95} </math> |
coloured_jones_6 = <math>q^{57}-5 q^{56}+3 q^{55}+14 q^{54}-6 q^{53}-15 q^{52}-29 q^{51}+13 q^{50}+12 q^{49}+46 q^{48}+147 q^{47}-3 q^{46}-158 q^{45}-367 q^{44}-236 q^{43}-34 q^{42}+449 q^{41}+1244 q^{40}+970 q^{39}+22 q^{38}-1815 q^{37}-2711 q^{36}-2878 q^{35}-557 q^{34}+4314 q^{33}+7213 q^{32}+6891 q^{31}+501 q^{30}-7395 q^{29}-15758 q^{28}-15544 q^{27}-2539 q^{26}+15291 q^{25}+30283 q^{24}+27867 q^{23}+9228 q^{22}-26949 q^{21}-54410 q^{20}-51067 q^{19}-14516 q^{18}+43740 q^{17}+85559 q^{16}+88090 q^{15}+23123 q^{14}-69538 q^{13}-135402 q^{12}-128030 q^{11}-32561 q^{10}+100451 q^9+204585 q^8+178683 q^7+35402 q^6-155693 q^5-276577 q^4-233296 q^3-32602 q^2+235195 q+364754+277833 q^{-1} -6881 q^{-2} -320564 q^{-3} -458656 q^{-4} -308568 q^{-5} +84205 q^{-6} +434931 q^{-7} +537846 q^{-8} +282605 q^{-9} -181245 q^{-10} -564400 q^{-11} -594619 q^{-12} -198691 q^{-13} +330483 q^{-14} +680589 q^{-15} +575644 q^{-16} +75505 q^{-17} -510911 q^{-18} -770134 q^{-19} -479914 q^{-20} +125390 q^{-21} +682241 q^{-22} +768671 q^{-23} +326559 q^{-24} -371957 q^{-25} -822791 q^{-26} -674236 q^{-27} -74077 q^{-28} +610250 q^{-29} +857823 q^{-30} +505896 q^{-31} -233228 q^{-32} -810609 q^{-33} -785117 q^{-34} -222197 q^{-35} +529518 q^{-36} +892351 q^{-37} +625002 q^{-38} -120688 q^{-39} -780219 q^{-40} -855997 q^{-41} -340050 q^{-42} +448490 q^{-43} +904821 q^{-44} +724933 q^{-45} -3220 q^{-46} -725155 q^{-47} -908816 q^{-48} -468676 q^{-49} +326403 q^{-50} +875471 q^{-51} +818376 q^{-52} +160417 q^{-53} -595293 q^{-54} -909875 q^{-55} -610257 q^{-56} +123130 q^{-57} +744150 q^{-58} +855244 q^{-59} +358388 q^{-60} -353776 q^{-61} -787792 q^{-62} -694526 q^{-63} -130939 q^{-64} +479294 q^{-65} +752315 q^{-66} +496689 q^{-67} -53388 q^{-68} -518543 q^{-69} -626795 q^{-70} -317127 q^{-71} +157242 q^{-72} +496034 q^{-73} +472200 q^{-74} +165921 q^{-75} -200735 q^{-76} -406467 q^{-77} -330890 q^{-78} -69254 q^{-79} +203709 q^{-80} +300160 q^{-81} +208105 q^{-82} +11002 q^{-83} -163059 q^{-84} -206333 q^{-85} -122835 q^{-86} +20859 q^{-87} +114861 q^{-88} +126502 q^{-89} +64452 q^{-90} -22897 q^{-91} -75149 q^{-92} -72673 q^{-93} -26641 q^{-94} +17754 q^{-95} +42301 q^{-96} +36943 q^{-97} +11186 q^{-98} -12780 q^{-99} -22497 q^{-100} -14987 q^{-101} -3802 q^{-102} +6741 q^{-103} +10279 q^{-104} +6256 q^{-105} +262 q^{-106} -3713 q^{-107} -3366 q^{-108} -2142 q^{-109} +123 q^{-110} +1583 q^{-111} +1312 q^{-112} +386 q^{-113} -384 q^{-114} -310 q^{-115} -379 q^{-116} -105 q^{-117} +178 q^{-118} +147 q^{-119} +41 q^{-120} -65 q^{-121} +15 q^{-122} -28 q^{-123} -25 q^{-124} +24 q^{-125} +9 q^{-126} + q^{-127} -13 q^{-128} +5 q^{-129} +4 q^{-130} -4 q^{-131} + q^{-132} </math> |
coloured_jones_7 = <math>-q^{77}+5 q^{76}-3 q^{75}-14 q^{74}+6 q^{73}+15 q^{72}+29 q^{71}-8 q^{70}-42 q^{69}-17 q^{68}-65 q^{67}-62 q^{66}+53 q^{65}+205 q^{64}+363 q^{63}+225 q^{62}-207 q^{61}-526 q^{60}-1015 q^{59}-1076 q^{58}-339 q^{57}+997 q^{56}+2987 q^{55}+3770 q^{54}+2496 q^{53}-522 q^{52}-5407 q^{51}-9547 q^{50}-9986 q^{49}-5395 q^{48}+5972 q^{47}+18756 q^{46}+25994 q^{45}+22951 q^{44}+4388 q^{43}-23636 q^{42}-50025 q^{41}-61295 q^{40}-41189 q^{39}+8542 q^{38}+70522 q^{37}+118760 q^{36}+117895 q^{35}+55653 q^{34}-54766 q^{33}-175676 q^{32}-238141 q^{31}-195483 q^{30}-40511 q^{29}+182613 q^{28}+367971 q^{27}+414939 q^{26}+264128 q^{25}-66388 q^{24}-439265 q^{23}-676126 q^{22}-625966 q^{21}-238988 q^{20}+346214 q^{19}+880257 q^{18}+1082336 q^{17}+766515 q^{16}+7574 q^{15}-897258 q^{14}-1516157 q^{13}-1465900 q^{12}-673337 q^{11}+590454 q^{10}+1764879 q^9+2213668 q^8+1615593 q^7+112556 q^6-1665147 q^5-2822242 q^4-2705364 q^3-1198124 q^2+1111249 q+3106578+3748955 q^{-1} +2546754 q^{-2} -94561 q^{-3} -2932065 q^{-4} -4544974 q^{-5} -3970524 q^{-6} -1287412 q^{-7} +2263048 q^{-8} +4937335 q^{-9} +5261483 q^{-10} +2864862 q^{-11} -1165051 q^{-12} -4862053 q^{-13} -6252848 q^{-14} -4436603 q^{-15} -216180 q^{-16} +4347929 q^{-17} +6850240 q^{-18} +5831383 q^{-19} +1705045 q^{-20} -3503822 q^{-21} -7049080 q^{-22} -6936254 q^{-23} -3133803 q^{-24} +2474147 q^{-25} +6911668 q^{-26} +7711927 q^{-27} +4384567 q^{-28} -1402181 q^{-29} -6544746 q^{-30} -8182962 q^{-31} -5395536 q^{-32} +402193 q^{-33} +6060211 q^{-34} +8413636 q^{-35} +6161476 q^{-36} +459355 q^{-37} -5553743 q^{-38} -8486939 q^{-39} -6718006 q^{-40} -1160176 q^{-41} +5090863 q^{-42} +8479451 q^{-43} +7122092 q^{-44} +1717549 q^{-45} -4698297 q^{-46} -8450748 q^{-47} -7440451 q^{-48} -2175554 q^{-49} +4371827 q^{-50} +8435186 q^{-51} +7730287 q^{-52} +2592903 q^{-53} -4075215 q^{-54} -8436095 q^{-55} -8035187 q^{-56} -3034014 q^{-57} +3751721 q^{-58} +8428340 q^{-59} +8372101 q^{-60} +3552214 q^{-61} -3331008 q^{-62} -8354428 q^{-63} -8723609 q^{-64} -4181694 q^{-65} +2741764 q^{-66} +8135949 q^{-67} +9036407 q^{-68} +4916830 q^{-69} -1934342 q^{-70} -7682771 q^{-71} -9218072 q^{-72} -5704977 q^{-73} +895583 q^{-74} +6919798 q^{-75} +9157727 q^{-76} +6443244 q^{-77} +325035 q^{-78} -5814345 q^{-79} -8747457 q^{-80} -6991824 q^{-81} -1614595 q^{-82} +4400454 q^{-83} +7923098 q^{-84} +7207331 q^{-85} +2808350 q^{-86} -2793574 q^{-87} -6695555 q^{-88} -6984368 q^{-89} -3725086 q^{-90} +1175115 q^{-91} +5165363 q^{-92} +6297475 q^{-93} +4219104 q^{-94} +249033 q^{-95} -3513648 q^{-96} -5223160 q^{-97} -4225837 q^{-98} -1299571 q^{-99} +1957131 q^{-100} +3922146 q^{-101} +3786854 q^{-102} +1882299 q^{-103} -686673 q^{-104} -2604575 q^{-105} -3040392 q^{-106} -2006206 q^{-107} -180061 q^{-108} +1460192 q^{-109} +2170262 q^{-110} +1779506 q^{-111} +632115 q^{-112} -611740 q^{-113} -1356868 q^{-114} -1360872 q^{-115} -744407 q^{-116} +90916 q^{-117} +718366 q^{-118} +903805 q^{-119} +644597 q^{-120} +152790 q^{-121} -297183 q^{-122} -519690 q^{-123} -458776 q^{-124} -208683 q^{-125} +70313 q^{-126} +252753 q^{-127} +276253 q^{-128} +172482 q^{-129} +22452 q^{-130} -99576 q^{-131} -142875 q^{-132} -110794 q^{-133} -40805 q^{-134} +27835 q^{-135} +62462 q^{-136} +58792 q^{-137} +31757 q^{-138} -1907 q^{-139} -23120 q^{-140} -26826 q^{-141} -17943 q^{-142} -3253 q^{-143} +7031 q^{-144} +10225 q^{-145} +8202 q^{-146} +2835 q^{-147} -1570 q^{-148} -3579 q^{-149} -3419 q^{-150} -1222 q^{-151} +433 q^{-152} +998 q^{-153} +1045 q^{-154} +463 q^{-155} +52 q^{-156} -281 q^{-157} -454 q^{-158} -122 q^{-159} +84 q^{-160} +79 q^{-161} +64 q^{-162} -3 q^{-163} +25 q^{-164} +5 q^{-165} -60 q^{-166} -5 q^{-167} +20 q^{-168} +9 q^{-169} + q^{-170} -13 q^{-171} +5 q^{-172} +4 q^{-173} -4 q^{-174} + q^{-175} </math> |
computer_talk = 
         <table>
         <tr valign=top>
         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; 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[9, 40]]</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[7, 12, 8, 13], X[5, 15, 6, 14], X[11, 3, 12, 2], 
 
  X[15, 10, 16, 11], X[3, 16, 4, 17], X[9, 4, 10, 5], X[17, 9, 18, 8], 
 
  X[13, 18, 14, 1]]</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[9, 40]]</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, 4, -6, 7, -3, 1, -2, 8, -7, 5, -4, 2, -9, 3, -5, 6, -8, 9]</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[9, 40]]</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, 16, 14, 12, 4, 2, 18, 10, 8]</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[9, 40]]</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, 2, -1, -3, 2, -1, -3, 2, -3}]</nowiki></code></td></tr>
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<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>
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<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, 9}</nowiki></code></td></tr>
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<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[9, 40]]</nowiki></code></td></tr>
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<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>
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<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[9, 40]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:9_40_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>
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<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[9, 40]]&) /@ {
                  SymmetryType, UnknottingNumber, ThreeGenus,
                  BridgeIndex, SuperBridgeIndex, NakanishiIndex
                 }</nowiki></code></td></tr>
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<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>{Reversible, 2, 3, 3, 4, 2}</nowiki></code></td></tr>
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<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[9, 40]][t]</nowiki></code></td></tr>
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<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>       -3   7    18             2    3
-23 + t   - -- + -- + 18 t - 7 t  + t
             2   t
            t</nowiki></code></td></tr>
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<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[9, 40]][z]</nowiki></code></td></tr>
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<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  - z  + z</nowiki></code></td></tr>
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<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>
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<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[9, 40], Knot[10, 59], Knot[11, NonAlternating, 66]}</nowiki></code></td></tr>
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<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[9, 40]], KnotSignature[Knot[9, 40]]}</nowiki></code></td></tr>
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<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>{75, -2}</nowiki></code></td></tr>
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<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[9, 40]][q]</nowiki></code></td></tr>
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<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>      -7   4    8    11   13   13   11          2
-8 + q   - -- + -- - -- + -- - -- + -- + 5 q - q
            6    5    4    3    2   q
           q    q    q    q    q</nowiki></code></td></tr>
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<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>
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<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[9, 40]}</nowiki></code></td></tr>
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<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[9, 40]][q]</nowiki></code></td></tr>
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<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>     -22    -20    2     3     -14    2     -10   3     -6   4    3
1 + q    - q    - --- + --- - q    + --- + q    - -- + q   - -- + -- + 
                   18    16           12           8          4    2
                  q     q            q            q          q    q
 
     4    6
  3 q  - q</nowiki></code></td></tr>
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<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[9, 40]][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>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       2    4      4  2    6  2    4      2  4      4  4    2  6
2 - 2 a  + a  - 2 a  z  + a  z  - z  + 2 a  z  - 2 a  z  + 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>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[9, 40]][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>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       2    4    3      5        2  2      4  2      6  2        3
2 + 2 a  + a  - a  z - a  z + 3 a  z  + 7 a  z  + 4 a  z  + 6 a z  + 
 
      3  3      5  3      7  3      4       2  4       4  4      6  4
  14 a  z  + 6 a  z  - 2 a  z  - 7 z  - 17 a  z  - 20 a  z  - 9 a  z  + 
 
           5
   8  4   z          5       3  5       5  5      7  5      6
  a  z  + -- - 15 a z  - 32 a  z  - 12 a  z  + 4 a  z  + 5 z  + 
          a
 
     2  6      4  6      6  6        7       3  7      5  7      2  8
  4 a  z  + 7 a  z  + 8 a  z  + 8 a z  + 17 a  z  + 9 a  z  + 4 a  z  + 
 
     4  8
  4 a  z</nowiki></code></td></tr>
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<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[9, 40]], Vassiliev[3][Knot[9, 40]]}</nowiki></code></td></tr>
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<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, 1}</nowiki></code></td></tr>
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<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[9, 40]][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>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>5    7     1        3        1        5        3       6       5
-- + - + ------ + ------ + ------ + ------ + ----- + ----- + ----- + 
 3   q    15  6    13  5    11  5    11  4    9  4    9  3    7  3
q        q   t    q   t    q   t    q   t    q  t    q  t    q  t
 
    7       6      6      7     4 t              2      3  2    5  3
  ----- + ----- + ---- + ---- + --- + 4 q t + q t  + 4 q  t  + q  t
   7  2    5  2    5      3      q
  q  t    q  t    q  t   q  t</nowiki></code></td></tr>
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<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[9, 40], 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>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       -20    4     4     9    29    17    45    84    17    107
-55 + q    - --- + --- + --- - --- + --- + --- - --- + --- + --- - 
              19    18    17    16    15    14    13    12    11
             q     q     q     q     q     q     q     q     q
 
  132   5    157   140   34   166   109   55   133   56
  --- - -- + --- - --- - -- + --- - --- - -- + --- - -- + 72 q - 
   10    9    8     7     6    5     4     3    2    q
  q     q    q     q     q    q     q     q    q
 
      2       3       4      5      6    7
  11 q  - 31 q  + 19 q  + 3 q  - 5 q  + q</nowiki></code></td></tr>
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