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http://myurl.com.tw/apjp
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{{Rolfsen Knot Page|
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n = 10 |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-7,6,-3,4,-2,9,-10,5,-6,7,-5,8,-9,10,-8/goTop.html |
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braid_table = <table cellspacing=0 cellpadding=0 border=0>
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<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.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]]</td></tr>
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<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
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</table> |
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braid_crossings = 12 |
braid_width = 5 |
braid_index = 5 |
same_alexander = |
same_jones = [[10_83]], |
khovanov_table = <table border=1>
<tr align=center>
<td width=13.3333%><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=6.66667%>-7</td ><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=13.3333%>&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>&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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&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>&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>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>4</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 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>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>7</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>&nbsp;</td><td bgcolor=yellow>2</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>&nbsp;</td><td>4</td></tr>
<tr align=center><td>-13</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</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>&nbsp;</td><td bgcolor=yellow>2</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>2</td></tr>
<tr align=center><td>-17</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>&nbsp;</td><td>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^7-4 q^6+2 q^5+13 q^4-24 q^3-q^2+52 q-57-24 q^{-1} +113 q^{-2} -83 q^{-3} -64 q^{-4} +166 q^{-5} -86 q^{-6} -100 q^{-7} +182 q^{-8} -66 q^{-9} -111 q^{-10} +151 q^{-11} -32 q^{-12} -90 q^{-13} +90 q^{-14} -6 q^{-15} -50 q^{-16} +36 q^{-17} +2 q^{-18} -17 q^{-19} +9 q^{-20} + q^{-21} -3 q^{-22} + q^{-23} </math> |
coloured_jones_3 = <math>-q^{15}+4 q^{14}-2 q^{13}-8 q^{12}+23 q^{10}+7 q^9-54 q^8-20 q^7+90 q^6+66 q^5-144 q^4-136 q^3+188 q^2+252 q-229-384 q^{-1} +223 q^{-2} +558 q^{-3} -206 q^{-4} -711 q^{-5} +136 q^{-6} +869 q^{-7} -57 q^{-8} -981 q^{-9} -52 q^{-10} +1068 q^{-11} +152 q^{-12} -1098 q^{-13} -257 q^{-14} +1086 q^{-15} +344 q^{-16} -1019 q^{-17} -418 q^{-18} +911 q^{-19} +464 q^{-20} -767 q^{-21} -476 q^{-22} +600 q^{-23} +454 q^{-24} -431 q^{-25} -405 q^{-26} +288 q^{-27} +324 q^{-28} -167 q^{-29} -242 q^{-30} +87 q^{-31} +164 q^{-32} -40 q^{-33} -100 q^{-34} +15 q^{-35} +56 q^{-36} -5 q^{-37} -28 q^{-38} + q^{-39} +14 q^{-40} -2 q^{-41} -4 q^{-42} - q^{-43} +3 q^{-44} - q^{-45} </math> |
coloured_jones_4 = <math>q^{26}-4 q^{25}+2 q^{24}+8 q^{23}-5 q^{22}+q^{21}-29 q^{20}+11 q^{19}+55 q^{18}-5 q^{17}-152 q^{15}-8 q^{14}+212 q^{13}+98 q^{12}+60 q^{11}-508 q^{10}-242 q^9+440 q^8+503 q^7+480 q^6-1085 q^5-1009 q^4+376 q^3+1218 q^2+1680 q-1451-2333 q^{-1} -503 q^{-2} +1779 q^{-3} +3695 q^{-4} -1036 q^{-5} -3700 q^{-6} -2259 q^{-7} +1625 q^{-8} +5921 q^{-9} +247 q^{-10} -4465 q^{-11} -4334 q^{-12} +673 q^{-13} +7619 q^{-14} +1912 q^{-15} -4414 q^{-16} -6034 q^{-17} -684 q^{-18} +8387 q^{-19} +3403 q^{-20} -3688 q^{-21} -6972 q^{-22} -2056 q^{-23} +8149 q^{-24} +4423 q^{-25} -2462 q^{-26} -6996 q^{-27} -3227 q^{-28} +6905 q^{-29} +4805 q^{-30} -896 q^{-31} -6039 q^{-32} -3954 q^{-33} +4846 q^{-34} +4359 q^{-35} +599 q^{-36} -4246 q^{-37} -3896 q^{-38} +2562 q^{-39} +3129 q^{-40} +1445 q^{-41} -2230 q^{-42} -2996 q^{-43} +860 q^{-44} +1636 q^{-45} +1401 q^{-46} -748 q^{-47} -1737 q^{-48} +89 q^{-49} +543 q^{-50} +859 q^{-51} -85 q^{-52} -751 q^{-53} -48 q^{-54} +68 q^{-55} +360 q^{-56} +50 q^{-57} -249 q^{-58} -9 q^{-59} -28 q^{-60} +108 q^{-61} +28 q^{-62} -69 q^{-63} +10 q^{-64} -16 q^{-65} +24 q^{-66} +7 q^{-67} -17 q^{-68} +5 q^{-69} -3 q^{-70} +4 q^{-71} + q^{-72} -3 q^{-73} + q^{-74} </math> |
coloured_jones_5 = <math>-q^{40}+4 q^{39}-2 q^{38}-8 q^{37}+5 q^{36}+4 q^{35}+5 q^{34}+11 q^{33}-12 q^{32}-46 q^{31}-9 q^{30}+46 q^{29}+70 q^{28}+58 q^{27}-59 q^{26}-196 q^{25}-173 q^{24}+97 q^{23}+390 q^{22}+391 q^{21}-15 q^{20}-651 q^{19}-914 q^{18}-259 q^{17}+1010 q^{16}+1696 q^{15}+912 q^{14}-1114 q^{13}-2891 q^{12}-2289 q^{11}+925 q^{10}+4257 q^9+4402 q^8+221 q^7-5555 q^6-7475 q^5-2442 q^4+6246 q^3+11080 q^2+6278 q-5903-14951 q^{-1} -11356 q^{-2} +3868 q^{-3} +18322 q^{-4} +17773 q^{-5} -194 q^{-6} -20792 q^{-7} -24457 q^{-8} -5299 q^{-9} +21650 q^{-10} +31323 q^{-11} +11920 q^{-12} -21046 q^{-13} -37171 q^{-14} -19299 q^{-15} +18749 q^{-16} +42086 q^{-17} +26651 q^{-18} -15444 q^{-19} -45385 q^{-20} -33551 q^{-21} +11246 q^{-22} +47465 q^{-23} +39498 q^{-24} -6773 q^{-25} -48110 q^{-26} -44442 q^{-27} +2144 q^{-28} +47752 q^{-29} +48204 q^{-30} +2362 q^{-31} -46231 q^{-32} -50921 q^{-33} -6851 q^{-34} +43817 q^{-35} +52489 q^{-36} +11196 q^{-37} -40256 q^{-38} -52905 q^{-39} -15480 q^{-40} +35634 q^{-41} +52032 q^{-42} +19450 q^{-43} -29929 q^{-44} -49654 q^{-45} -22892 q^{-46} +23333 q^{-47} +45717 q^{-48} +25424 q^{-49} -16288 q^{-50} -40284 q^{-51} -26595 q^{-52} +9323 q^{-53} +33617 q^{-54} +26204 q^{-55} -3051 q^{-56} -26358 q^{-57} -24226 q^{-58} -1794 q^{-59} +19035 q^{-60} +20888 q^{-61} +5075 q^{-62} -12471 q^{-63} -16808 q^{-64} -6549 q^{-65} +7145 q^{-66} +12442 q^{-67} +6661 q^{-68} -3302 q^{-69} -8502 q^{-70} -5779 q^{-71} +923 q^{-72} +5298 q^{-73} +4429 q^{-74} +299 q^{-75} -2979 q^{-76} -3059 q^{-77} -735 q^{-78} +1510 q^{-79} +1909 q^{-80} +717 q^{-81} -662 q^{-82} -1086 q^{-83} -531 q^{-84} +240 q^{-85} +559 q^{-86} +343 q^{-87} -68 q^{-88} -279 q^{-89} -170 q^{-90} +13 q^{-91} +100 q^{-92} +98 q^{-93} +9 q^{-94} -64 q^{-95} -30 q^{-96} +10 q^{-97} +4 q^{-98} +16 q^{-99} +9 q^{-100} -19 q^{-101} -3 q^{-102} +9 q^{-103} -2 q^{-104} +3 q^{-106} -4 q^{-107} - q^{-108} +3 q^{-109} - q^{-110} </math> |
coloured_jones_6 = <math>q^{57}-4 q^{56}+2 q^{55}+8 q^{54}-5 q^{53}-4 q^{52}-10 q^{51}+13 q^{50}-10 q^{49}+3 q^{48}+60 q^{47}-21 q^{46}-40 q^{45}-80 q^{44}+22 q^{43}-5 q^{42}+61 q^{41}+286 q^{40}+12 q^{39}-178 q^{38}-448 q^{37}-157 q^{36}-135 q^{35}+324 q^{34}+1215 q^{33}+621 q^{32}-195 q^{31}-1615 q^{30}-1455 q^{29}-1478 q^{28}+365 q^{27}+3740 q^{26}+3768 q^{25}+1917 q^{24}-2962 q^{23}-5348 q^{22}-7543 q^{21}-3334 q^{20}+6610 q^{19}+12056 q^{18}+11873 q^{17}+1241 q^{16}-9581 q^{15}-22247 q^{14}-19489 q^{13}+803 q^{12}+21987 q^{11}+34991 q^{10}+23437 q^9-1149 q^8-40193 q^7-54756 q^6-30334 q^5+16101 q^4+63341 q^3+71447 q^2+40497 q-39205-98262 q^{-1} -95029 q^{-2} -29381 q^{-3} +70285 q^{-4} +131292 q^{-5} +122734 q^{-6} +6659 q^{-7} -119636 q^{-8} -175737 q^{-9} -120110 q^{-10} +29122 q^{-11} +169919 q^{-12} +224103 q^{-13} +100467 q^{-14} -92576 q^{-15} -237228 q^{-16} -231371 q^{-17} -60200 q^{-18} +162216 q^{-19} +307836 q^{-20} +215010 q^{-21} -19462 q^{-22} -255369 q^{-23} -326396 q^{-24} -169328 q^{-25} +111873 q^{-26} +350715 q^{-27} +314825 q^{-28} +72448 q^{-29} -233442 q^{-30} -383771 q^{-31} -265787 q^{-32} +42953 q^{-33} +354768 q^{-34} +381039 q^{-35} +155815 q^{-36} -190614 q^{-37} -404833 q^{-38} -334412 q^{-39} -23710 q^{-40} +334111 q^{-41} +414974 q^{-42} +220484 q^{-43} -140794 q^{-44} -399768 q^{-45} -377429 q^{-46} -83357 q^{-47} +296595 q^{-48} +423848 q^{-49} +270326 q^{-50} -83847 q^{-51} -371723 q^{-52} -399730 q^{-53} -141303 q^{-54} +238295 q^{-55} +406706 q^{-56} +308004 q^{-57} -13867 q^{-58} -313815 q^{-59} -396214 q^{-60} -197255 q^{-61} +153731 q^{-62} +353656 q^{-63} +323626 q^{-64} +64742 q^{-65} -221298 q^{-66} -353478 q^{-67} -235511 q^{-68} +52358 q^{-69} +260334 q^{-70} +299383 q^{-71} +129465 q^{-72} -108265 q^{-73} -266947 q^{-74} -233351 q^{-75} -36508 q^{-76} +144548 q^{-77} +229746 q^{-78} +152717 q^{-79} -8930 q^{-80} -157047 q^{-81} -184327 q^{-82} -81848 q^{-83} +43312 q^{-84} +136431 q^{-85} +127673 q^{-86} +45298 q^{-87} -61599 q^{-88} -110955 q^{-89} -77876 q^{-90} -13719 q^{-91} +56081 q^{-92} +77222 q^{-93} +51529 q^{-94} -7043 q^{-95} -47644 q^{-96} -47814 q^{-97} -26772 q^{-98} +10952 q^{-99} +32755 q^{-100} +33170 q^{-101} +9375 q^{-102} -12557 q^{-103} -19668 q^{-104} -18099 q^{-105} -3439 q^{-106} +8773 q^{-107} +14550 q^{-108} +7515 q^{-109} -718 q^{-110} -4963 q^{-111} -7712 q^{-112} -3764 q^{-113} +824 q^{-114} +4639 q^{-115} +3006 q^{-116} +889 q^{-117} -360 q^{-118} -2299 q^{-119} -1624 q^{-120} -432 q^{-121} +1179 q^{-122} +725 q^{-123} +367 q^{-124} +299 q^{-125} -504 q^{-126} -453 q^{-127} -249 q^{-128} +291 q^{-129} +88 q^{-130} +43 q^{-131} +162 q^{-132} -85 q^{-133} -89 q^{-134} -77 q^{-135} +87 q^{-136} -6 q^{-137} -20 q^{-138} +48 q^{-139} -14 q^{-140} -10 q^{-141} -19 q^{-142} +26 q^{-143} -2 q^{-144} -13 q^{-145} +10 q^{-146} -3 q^{-147} -3 q^{-149} +4 q^{-150} + q^{-151} -3 q^{-152} + q^{-153} </math> |
coloured_jones_7 = |
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[10, 73]]</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[4, 2, 5, 1], X[10, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10],
X[16, 14, 17, 13], X[14, 7, 15, 8], X[6, 15, 7, 16],
X[20, 17, 1, 18], X[18, 11, 19, 12], X[12, 19, 13, 20]]</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, 73]]</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, 3, -1, 2, -7, 6, -3, 4, -2, 9, -10, 5, -6, 7, -5, 8,
-9, 10, -8]</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, 73]]</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[4, 8, 10, 14, 2, 18, 16, 6, 20, 12]</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, 73]]</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[5, {-1, -1, -2, 1, -2, -1, 3, -2, 3, -4, 3, -4}]</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>{5, 12}</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, 73]]</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>5</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, 73]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_73_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, 73]]&) /@ {
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>{Reversible, 1, 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, 73]][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> -3 7 20 2 3
-27 + t - -- + -- + 20 t - 7 t + t
2 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, 73]][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 - z + 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, 73]}</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, 73]], KnotSignature[Knot[10, 73]]}</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, 73]][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> -8 3 6 10 13 14 13 11 2
-7 - q + -- - -- + -- - -- + -- - -- + -- + 4 q - q
7 6 5 4 3 2 q
q q q 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, 73]][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> -26 -24 2 3 3 -10 -8 3 2 4 2
-q - q + --- + --- - --- - q - q + -- - -- + -- - q +
22 16 14 6 4 2
q q q q q q
4 6
2 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, 73]][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 4 6 8 2 2 2 4 2 6 2 4
3 a - 4 a + 3 a - a - z + 5 a z - 6 a z + 3 a z - z +
2 4 4 4 2 6
3 a z - 3 a z + a z</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, 73]][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 4 6 8 3 5 9 2
-3 a - 4 a - 3 a - a - a z - 3 a z - 3 a z + a z + 3 z +
3
2 2 4 2 6 2 8 2 z 3 3 3
12 a z + 17 a z + 12 a z + 4 a z - -- + 4 a z + 16 a z +
a
5 3 7 3 9 3 4 2 4 4 4 6 4
14 a z + a z - 2 a z - 7 z - 16 a z - 17 a z - 14 a z -
5
8 4 z 5 3 5 5 5 7 5 9 5
6 a z + -- - 10 a z - 26 a z - 21 a z - 5 a z + a z +
a
6 2 6 4 6 6 6 8 6 7 3 7
4 z + 2 a z - 2 a z + 3 a z + 3 a z + 6 a z + 12 a z +
5 7 7 7 2 8 4 8 6 8 3 9 5 9
10 a z + 4 a z + 4 a z + 7 a z + 3 a z + a z + a z</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, 73]], Vassiliev[3][Knot[10, 73]]}</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, 73]][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>5 7 1 2 1 4 2 6 4
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ----- +
3 q 17 7 15 6 13 6 13 5 11 5 11 4 9 4
q q t q t q t q t q t q t q t
7 6 7 7 6 7 3 t 2
----- + ----- + ----- + ----- + ---- + ---- + --- + 4 q t + q t +
9 3 7 3 7 2 5 2 5 3 q
q t q t q t q t q t q t
3 2 5 3
3 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, 73], 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> -23 3 -21 9 17 2 36 50 6 90
-57 + q - --- + q + --- - --- + --- + --- - --- - --- + --- -
22 20 19 18 17 16 15 14
q q q q q q q q
90 32 151 111 66 182 100 86 166 64 83 113
--- - --- + --- - --- - -- + --- - --- - -- + --- - -- - -- + --- -
13 12 11 10 9 8 7 6 5 4 3 2
q q q q q q q q q q q q
24 2 3 4 5 6 7
-- + 52 q - q - 24 q + 13 q + 2 q - 4 q + q
q</nowiki></code></td></tr>
</table> }}

Revision as of 20:30, 9 March 2007

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