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{{Rolfsen Knot Page| |
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n = 10 | |
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k = 100 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,5,-7,2,-1,4,-8,6,-5,7,-9,3,-4,8,-6,10,-2,9,-3/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:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr> |
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{{Rolfsen Knot Page Header|n=10|k=100|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,5,-7,2,-1,4,-8,6,-5,7,-9,3,-4,8,-6,10,-2,9,-3/goTop.html}} |
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braid_crossings = 10 | |
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braid_width = 3 | |
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braid_index = 3 | |
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{{:{{PAGENAME}} Further Notes and Views}} |
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same_alexander = | |
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same_jones = | |
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{{Knot Presentations}} |
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khovanov_table = <table border=1> |
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{{3D Invariants}} |
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{{4D Invariants}} |
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{{Vassiliev Invariants}} |
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{{Khovanov Homology|table=<table border=1> |
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<tr><td>\</td><td> </td><td>r</td></tr> |
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<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%>χ</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> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td>-1</td></tr> |
<tr align=center><td>3</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>1</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>1</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> |
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<tr align=center><td>-17</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>-19</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> |
<tr align=center><td>-19</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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coloured_jones_2 = <math>q^5-3 q^4-q^3+11 q^2-9 q-14+30 q^{-1} -5 q^{-2} -40 q^{-3} +45 q^{-4} +12 q^{-5} -66 q^{-6} +47 q^{-7} +33 q^{-8} -81 q^{-9} +37 q^{-10} +49 q^{-11} -77 q^{-12} +19 q^{-13} +51 q^{-14} -57 q^{-15} +7 q^{-16} +34 q^{-17} -32 q^{-18} +6 q^{-19} +13 q^{-20} -14 q^{-21} +4 q^{-22} +3 q^{-23} -3 q^{-24} + q^{-25} </math> | |
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{{Computer Talk Header}} |
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coloured_jones_3 = <math>-q^{12}+3 q^{11}+q^{10}-5 q^9-9 q^8+9 q^7+23 q^6-6 q^5-42 q^4-12 q^3+61 q^2+44 q-68-87 q^{-1} +57 q^{-2} +128 q^{-3} -20 q^{-4} -166 q^{-5} -20 q^{-6} +175 q^{-7} +80 q^{-8} -178 q^{-9} -123 q^{-10} +151 q^{-11} +176 q^{-12} -131 q^{-13} -198 q^{-14} +80 q^{-15} +236 q^{-16} -48 q^{-17} -242 q^{-18} -14 q^{-19} +261 q^{-20} +54 q^{-21} -246 q^{-22} -107 q^{-23} +227 q^{-24} +138 q^{-25} -186 q^{-26} -151 q^{-27} +137 q^{-28} +141 q^{-29} -91 q^{-30} -107 q^{-31} +48 q^{-32} +74 q^{-33} -31 q^{-34} -33 q^{-35} +14 q^{-36} +13 q^{-37} -12 q^{-38} + q^{-39} +9 q^{-40} -5 q^{-41} -6 q^{-42} +5 q^{-43} +2 q^{-44} - q^{-45} -3 q^{-46} +3 q^{-47} - q^{-48} </math> | |
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coloured_jones_4 = <math>q^{22}-3 q^{21}-q^{20}+5 q^{19}+3 q^{18}+9 q^{17}-19 q^{16}-21 q^{15}+4 q^{14}+18 q^{13}+73 q^{12}-14 q^{11}-74 q^{10}-74 q^9-43 q^8+189 q^7+118 q^6-9 q^5-179 q^4-310 q^3+135 q^2+258 q+302-16 q^{-1} -577 q^{-2} -199 q^{-3} +55 q^{-4} +576 q^{-5} +475 q^{-6} -457 q^{-7} -459 q^{-8} -503 q^{-9} +417 q^{-10} +888 q^{-11} +35 q^{-12} -276 q^{-13} -997 q^{-14} -117 q^{-15} +875 q^{-16} +503 q^{-17} +272 q^{-18} -1126 q^{-19} -676 q^{-20} +515 q^{-21} +725 q^{-22} +875 q^{-23} -976 q^{-24} -1082 q^{-25} +59 q^{-26} +785 q^{-27} +1394 q^{-28} -724 q^{-29} -1402 q^{-30} -420 q^{-31} +790 q^{-32} +1865 q^{-33} -364 q^{-34} -1629 q^{-35} -962 q^{-36} +618 q^{-37} +2192 q^{-38} +176 q^{-39} -1527 q^{-40} -1401 q^{-41} +147 q^{-42} +2059 q^{-43} +679 q^{-44} -966 q^{-45} -1372 q^{-46} -372 q^{-47} +1399 q^{-48} +769 q^{-49} -308 q^{-50} -857 q^{-51} -526 q^{-52} +651 q^{-53} +454 q^{-54} +25 q^{-55} -308 q^{-56} -348 q^{-57} +220 q^{-58} +133 q^{-59} +58 q^{-60} -42 q^{-61} -144 q^{-62} +70 q^{-63} + q^{-64} +22 q^{-65} +16 q^{-66} -45 q^{-67} +25 q^{-68} -14 q^{-69} +4 q^{-70} +11 q^{-71} -12 q^{-72} +7 q^{-73} -5 q^{-74} + q^{-75} +3 q^{-76} -3 q^{-77} + q^{-78} </math> | |
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coloured_jones_5 = <math>-q^{35}+3 q^{34}+q^{33}-5 q^{32}-3 q^{31}-3 q^{30}+q^{29}+17 q^{28}+24 q^{27}-6 q^{26}-31 q^{25}-48 q^{24}-40 q^{23}+26 q^{22}+112 q^{21}+122 q^{20}+24 q^{19}-121 q^{18}-243 q^{17}-206 q^{16}+44 q^{15}+342 q^{14}+443 q^{13}+215 q^{12}-249 q^{11}-671 q^{10}-652 q^9-91 q^8+674 q^7+1078 q^6+722 q^5-276 q^4-1279 q^3-1450 q^2-524 q+973+1964 q^{-1} +1571 q^{-2} -94 q^{-3} -1921 q^{-4} -2522 q^{-5} -1235 q^{-6} +1193 q^{-7} +2958 q^{-8} +2616 q^{-9} +250 q^{-10} -2625 q^{-11} -3730 q^{-12} -1978 q^{-13} +1483 q^{-14} +4064 q^{-15} +3720 q^{-16} +336 q^{-17} -3658 q^{-18} -4973 q^{-19} -2373 q^{-20} +2339 q^{-21} +5597 q^{-22} +4405 q^{-23} -594 q^{-24} -5419 q^{-25} -6012 q^{-26} -1527 q^{-27} +4687 q^{-28} +7169 q^{-29} +3472 q^{-30} -3456 q^{-31} -7762 q^{-32} -5360 q^{-33} +2160 q^{-34} +8050 q^{-35} +6763 q^{-36} -792 q^{-37} -8035 q^{-38} -8111 q^{-39} -347 q^{-40} +8105 q^{-41} +9112 q^{-42} +1424 q^{-43} -8110 q^{-44} -10298 q^{-45} -2413 q^{-46} +8284 q^{-47} +11412 q^{-48} +3555 q^{-49} -8266 q^{-50} -12688 q^{-51} -4934 q^{-52} +8002 q^{-53} +13762 q^{-54} +6582 q^{-55} -7130 q^{-56} -14466 q^{-57} -8317 q^{-58} +5626 q^{-59} +14382 q^{-60} +9866 q^{-61} -3574 q^{-62} -13381 q^{-63} -10792 q^{-64} +1287 q^{-65} +11479 q^{-66} +10834 q^{-67} +784 q^{-68} -8957 q^{-69} -9955 q^{-70} -2276 q^{-71} +6350 q^{-72} +8290 q^{-73} +2961 q^{-74} -3938 q^{-75} -6337 q^{-76} -2973 q^{-77} +2197 q^{-78} +4390 q^{-79} +2448 q^{-80} -1000 q^{-81} -2782 q^{-82} -1812 q^{-83} +392 q^{-84} +1625 q^{-85} +1158 q^{-86} -98 q^{-87} -871 q^{-88} -672 q^{-89} -3 q^{-90} +429 q^{-91} +359 q^{-92} +25 q^{-93} -209 q^{-94} -164 q^{-95} -10 q^{-96} +74 q^{-97} +72 q^{-98} +18 q^{-99} -36 q^{-100} -35 q^{-101} +9 q^{-102} +5 q^{-103} +2 q^{-104} +12 q^{-105} -5 q^{-106} -10 q^{-107} +7 q^{-108} -4 q^{-110} +5 q^{-111} - q^{-112} -3 q^{-113} +3 q^{-114} - q^{-115} </math> | |
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coloured_jones_6 = <math>q^{51}-3 q^{50}-q^{49}+5 q^{48}+3 q^{47}+3 q^{46}-7 q^{45}+q^{44}-20 q^{43}-22 q^{42}+18 q^{41}+32 q^{40}+54 q^{39}+17 q^{38}+24 q^{37}-86 q^{36}-160 q^{35}-102 q^{34}-15 q^{33}+166 q^{32}+224 q^{31}+391 q^{30}+113 q^{29}-258 q^{28}-525 q^{27}-650 q^{26}-359 q^{25}+24 q^{24}+1021 q^{23}+1208 q^{22}+912 q^{21}+48 q^{20}-1100 q^{19}-1901 q^{18}-2198 q^{17}-414 q^{16}+1196 q^{15}+2857 q^{14}+3158 q^{13}+1935 q^{12}-774 q^{11}-4189 q^{10}-4575 q^9-3674 q^8+66 q^7+4063 q^6+7085 q^5+6233 q^4+1007 q^3-3886 q^2-8910 q-8823-4563 q^{-1} +4088 q^{-2} +10812 q^{-3} +11568 q^{-4} +7941 q^{-5} -2435 q^{-6} -11642 q^{-7} -16653 q^{-8} -10863 q^{-9} +462 q^{-10} +12059 q^{-11} +20246 q^{-12} +15843 q^{-13} +3021 q^{-14} -14659 q^{-15} -22930 q^{-16} -20536 q^{-17} -6517 q^{-18} +14904 q^{-19} +27824 q^{-20} +26579 q^{-21} +7143 q^{-22} -14860 q^{-23} -32184 q^{-24} -31979 q^{-25} -10152 q^{-26} +18219 q^{-27} +38577 q^{-28} +34045 q^{-29} +12026 q^{-30} -21864 q^{-31} -44707 q^{-32} -38854 q^{-33} -8916 q^{-34} +29292 q^{-35} +48161 q^{-36} +41470 q^{-37} +4409 q^{-38} -37739 q^{-39} -55499 q^{-40} -37995 q^{-41} +5890 q^{-42} +44853 q^{-43} +60092 q^{-44} +32219 q^{-45} -18720 q^{-46} -57219 q^{-47} -57791 q^{-48} -18601 q^{-49} +31769 q^{-50} +66285 q^{-51} +52126 q^{-52} +705 q^{-53} -51330 q^{-54} -67584 q^{-55} -36242 q^{-56} +19279 q^{-57} +66989 q^{-58} +64101 q^{-59} +13966 q^{-60} -46977 q^{-61} -74086 q^{-62} -47917 q^{-63} +12406 q^{-64} +70217 q^{-65} +74952 q^{-66} +23461 q^{-67} -47139 q^{-68} -84229 q^{-69} -61197 q^{-70} +6384 q^{-71} +76463 q^{-72} +90562 q^{-73} +38096 q^{-74} -43936 q^{-75} -95495 q^{-76} -80913 q^{-77} -9354 q^{-78} +74515 q^{-79} +105117 q^{-80} +61282 q^{-81} -25684 q^{-82} -93598 q^{-83} -97744 q^{-84} -35952 q^{-85} +52783 q^{-86} +102074 q^{-87} +80059 q^{-88} +5225 q^{-89} -68569 q^{-90} -93965 q^{-91} -56804 q^{-92} +18130 q^{-93} +74510 q^{-94} +76731 q^{-95} +29011 q^{-96} -31931 q^{-97} -66571 q^{-98} -55462 q^{-99} -7782 q^{-100} +37948 q^{-101} +52390 q^{-102} +31575 q^{-103} -5501 q^{-104} -33548 q^{-105} -36543 q^{-106} -14076 q^{-107} +12598 q^{-108} +25511 q^{-109} +19968 q^{-110} +3357 q^{-111} -11984 q^{-112} -17113 q^{-113} -8931 q^{-114} +2563 q^{-115} +9132 q^{-116} +8461 q^{-117} +2804 q^{-118} -3173 q^{-119} -6102 q^{-120} -3416 q^{-121} +408 q^{-122} +2555 q^{-123} +2590 q^{-124} +1024 q^{-125} -685 q^{-126} -1828 q^{-127} -869 q^{-128} +165 q^{-129} +581 q^{-130} +601 q^{-131} +238 q^{-132} -111 q^{-133} -503 q^{-134} -137 q^{-135} +87 q^{-136} +93 q^{-137} +105 q^{-138} +38 q^{-139} +5 q^{-140} -133 q^{-141} + q^{-142} +33 q^{-143} - q^{-144} +15 q^{-145} +14 q^{-147} -33 q^{-148} +7 q^{-149} +11 q^{-150} -8 q^{-151} +5 q^{-152} -3 q^{-153} +4 q^{-154} -5 q^{-155} + q^{-156} +3 q^{-157} -3 q^{-158} + q^{-159} </math> | |
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:= </pre></td> |
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coloured_jones_7 = <math>-q^{70}+3 q^{69}+q^{68}-5 q^{67}-3 q^{66}-3 q^{65}+7 q^{64}+5 q^{63}+2 q^{62}+18 q^{61}+10 q^{60}-19 q^{59}-37 q^{58}-57 q^{57}-19 q^{56}+21 q^{55}+35 q^{54}+129 q^{53}+148 q^{52}+90 q^{51}-33 q^{50}-255 q^{49}-331 q^{48}-306 q^{47}-240 q^{46}+135 q^{45}+531 q^{44}+822 q^{43}+902 q^{42}+331 q^{41}-351 q^{40}-1082 q^{39}-1801 q^{38}-1675 q^{37}-887 q^{36}+594 q^{35}+2481 q^{34}+3305 q^{33}+3141 q^{32}+1716 q^{31}-1280 q^{30}-4032 q^{29}-6048 q^{28}-5905 q^{27}-2551 q^{26}+1939 q^{25}+6863 q^{24}+10172 q^{23}+9191 q^{22}+4772 q^{21}-3055 q^{20}-11456 q^{19}-15512 q^{18}-14675 q^{17}-7134 q^{16}+5222 q^{15}+16499 q^{14}+23890 q^{13}+21877 q^{12}+9574 q^{11}-7373 q^{10}-24986 q^9-34431 q^8-29957 q^7-13765 q^6+12090 q^5+36186 q^4+47182 q^3+41530 q^2+15958 q-19402-49857 q^{-1} -65083 q^{-2} -52873 q^{-3} -16683 q^{-4} +29530 q^{-5} +70934 q^{-6} +84897 q^{-7} +63940 q^{-8} +14944 q^{-9} -48647 q^{-10} -96339 q^{-11} -107287 q^{-12} -74535 q^{-13} -2772 q^{-14} +75648 q^{-15} +128401 q^{-16} +131983 q^{-17} +74415 q^{-18} -19990 q^{-19} -114058 q^{-20} -168422 q^{-21} -148442 q^{-22} -61435 q^{-23} +60412 q^{-24} +167961 q^{-25} +204298 q^{-26} +151895 q^{-27} +25933 q^{-28} -125159 q^{-29} -225990 q^{-30} -230552 q^{-31} -128449 q^{-32} +44437 q^{-33} +204456 q^{-34} +280149 q^{-35} +228649 q^{-36} +60896 q^{-37} -142361 q^{-38} -290647 q^{-39} -308145 q^{-40} -173431 q^{-41} +48992 q^{-42} +260535 q^{-43} +356125 q^{-44} +276725 q^{-45} +60699 q^{-46} -196377 q^{-47} -368133 q^{-48} -358483 q^{-49} -172267 q^{-50} +109201 q^{-51} +347223 q^{-52} +412503 q^{-53} +273413 q^{-54} -11247 q^{-55} -300528 q^{-56} -438577 q^{-57} -356821 q^{-58} -86156 q^{-59} +238061 q^{-60} +440210 q^{-61} +418790 q^{-62} +174939 q^{-63} -168592 q^{-64} -424114 q^{-65} -460763 q^{-66} -249571 q^{-67} +101431 q^{-68} +397494 q^{-69} +484738 q^{-70} +308019 q^{-71} -41797 q^{-72} -367946 q^{-73} -497145 q^{-74} -350626 q^{-75} -4641 q^{-76} +342478 q^{-77} +502989 q^{-78} +380158 q^{-79} +37481 q^{-80} -326356 q^{-81} -510555 q^{-82} -402564 q^{-83} -57203 q^{-84} +323256 q^{-85} +525503 q^{-86} +424782 q^{-87} +70086 q^{-88} -331531 q^{-89} -552941 q^{-90} -455861 q^{-91} -84629 q^{-92} +345996 q^{-93} +592280 q^{-94} +501423 q^{-95} +111798 q^{-96} -354985 q^{-97} -637206 q^{-98} -563173 q^{-99} -160559 q^{-100} +345245 q^{-101} +675023 q^{-102} +634500 q^{-103} +233991 q^{-104} -304978 q^{-105} -689433 q^{-106} -701239 q^{-107} -326167 q^{-108} +228796 q^{-109} +665983 q^{-110} +745503 q^{-111} +422166 q^{-112} -122490 q^{-113} -598036 q^{-114} -750002 q^{-115} -501621 q^{-116} +1263 q^{-117} +489838 q^{-118} +706307 q^{-119} +545985 q^{-120} +113150 q^{-121} -357059 q^{-122} -617571 q^{-123} -544252 q^{-124} -200247 q^{-125} +221449 q^{-126} +497696 q^{-127} +497335 q^{-128} +247922 q^{-129} -103703 q^{-130} -367730 q^{-131} -417546 q^{-132} -254086 q^{-133} +18061 q^{-134} +247180 q^{-135} +321981 q^{-136} +227682 q^{-137} +32574 q^{-138} -150026 q^{-139} -228985 q^{-140} -182686 q^{-141} -52355 q^{-142} +81540 q^{-143} +150082 q^{-144} +132689 q^{-145} +51937 q^{-146} -38838 q^{-147} -91351 q^{-148} -88419 q^{-149} -41165 q^{-150} +16208 q^{-151} +51860 q^{-152} +54076 q^{-153} +28017 q^{-154} -5736 q^{-155} -27676 q^{-156} -30779 q^{-157} -16908 q^{-158} +1878 q^{-159} +14207 q^{-160} +16429 q^{-161} +8993 q^{-162} -886 q^{-163} -7008 q^{-164} -8159 q^{-165} -4329 q^{-166} +551 q^{-167} +3438 q^{-168} +3997 q^{-169} +1849 q^{-170} -605 q^{-171} -1682 q^{-172} -1784 q^{-173} -628 q^{-174} +416 q^{-175} +731 q^{-176} +834 q^{-177} +228 q^{-178} -295 q^{-179} -387 q^{-180} -378 q^{-181} +23 q^{-182} +198 q^{-183} +96 q^{-184} +137 q^{-185} +12 q^{-186} -76 q^{-187} -62 q^{-188} -95 q^{-189} +45 q^{-190} +67 q^{-191} -15 q^{-192} +19 q^{-193} -7 q^{-194} -9 q^{-195} -25 q^{-197} +17 q^{-198} +14 q^{-199} -13 q^{-200} +7 q^{-201} -4 q^{-202} -2 q^{-203} +3 q^{-204} -4 q^{-205} +5 q^{-206} - q^{-207} -3 q^{-208} +3 q^{-209} - q^{-210} </math> | |
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<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
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computer_talk = |
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<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[10, 100]]</nowiki></pre></td></tr> |
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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 valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[14, 7, 15, 8], |
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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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<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, 100]]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[14, 7, 15, 8], |
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X[10, 3, 11, 4], X[16, 9, 17, 10], X[4, 11, 5, 12], X[8, 15, 9, 16], |
X[10, 3, 11, 4], X[16, 9, 17, 10], X[4, 11, 5, 12], X[8, 15, 9, 16], |
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X[12, 19, 13, 20], X[2, 18, 3, 17]]</nowiki></ |
X[12, 19, 13, 20], X[2, 18, 3, 17]]</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 100]]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -10, 5, -7, 2, -1, 4, -8, 6, -5, 7, -9, 3, -4, 8, -6, 10, |
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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, 100]]</nowiki></code></td></tr> |
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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, -10, 5, -7, 2, -1, 4, -8, 6, -5, 7, -9, 3, -4, 8, -6, 10, |
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-2, 9, -3]</nowiki></ |
-2, 9, -3]</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[10, 100]]</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {-1, -1, -1, 2, -1, -1, 2, -1, -1, 2}]</nowiki></pre></td></tr> |
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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, 100]]</nowiki></code></td></tr> |
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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[6, 10, 18, 14, 16, 4, 20, 8, 2, 12]</nowiki></code></td></tr> |
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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, 100]]</nowiki></code></td></tr> |
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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[3, {-1, -1, -1, 2, -1, -1, 2, -1, -1, 2}]</nowiki></code></td></tr> |
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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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<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>{3, 10}</nowiki></code></td></tr> |
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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, 100]]</nowiki></code></td></tr> |
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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>3</nowiki></code></td></tr> |
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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, 100]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:10_100_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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<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, 100]]&) /@ { |
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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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, {2, 3}, 4, 3, NotAvailable, 1}</nowiki></code></td></tr> |
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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, 100]][t]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 4 9 12 2 3 4 |
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13 + t - -- + -- - -- - 12 t + 9 t - 4 t + t |
13 + t - -- + -- - -- - 12 t + 9 t - 4 t + t |
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3 2 t |
3 2 t |
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t t</nowiki></ |
t t</nowiki></code></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 100]][z]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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1 + 4 z + 5 z + 4 z + z</nowiki></pre></td></tr> |
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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, 100]][z]</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 100]}</nowiki></pre></td></tr> |
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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 6 8 |
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1 + 4 z + 5 z + 4 z + z</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Knot[10, 100]][q]</nowiki></pre></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -9 3 6 8 10 11 9 8 5 |
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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, 100]}</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, 100]], KnotSignature[Knot[10, 100]]}</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, -4}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 100]][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> -9 3 6 8 10 11 9 8 5 |
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3 - q + -- - -- + -- - -- + -- - -- + -- - - - q |
3 - q + -- - -- + -- - -- + -- - -- + -- - - - q |
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8 7 6 5 4 3 2 q |
8 7 6 5 4 3 2 q |
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q q q q q q q</nowiki></ |
q q q q q q q</nowiki></code></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 100]}</nowiki></pre></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td> |
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<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr> |
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<tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -26 -24 2 -18 -16 3 -12 4 -6 -4 |
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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, 100]}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 100]][q]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -26 -24 2 -18 -16 3 -12 4 -6 -4 |
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1 - q + q - --- - q - q + --- - q + --- + q + q - |
1 - q + q - --- - q - q + --- - q + --- + q + q - |
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22 14 10 |
22 14 10 |
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Line 91: | Line 179: | ||
-2 2 |
-2 2 |
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q - q</nowiki></ |
q - q</nowiki></code></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 100]][a, z]</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 3 5 7 9 |
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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, 100]][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 4 6 2 2 4 2 6 2 2 4 4 4 |
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-a + 5 a - 3 a - 4 a z + 13 a z - 5 a z - 4 a z + 13 a z - |
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6 4 2 6 4 6 6 6 4 8 |
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4 a z - a z + 6 a z - a z + a 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[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, 100]][a, z]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6 3 5 7 9 |
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a + 5 a + 3 a - 2 a z - 6 a z - 8 a z - 2 a z + 2 a z - |
a + 5 a + 3 a - 2 a z - 6 a z - 8 a z - 2 a z + 2 a z - |
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Line 112: | Line 216: | ||
3 9 5 9 |
3 9 5 9 |
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2 a z + 2 a z</nowiki></ |
2 a z + 2 a z</nowiki></code></td></tr> |
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</table> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 100]], Vassiliev[3][Knot[10, 100]]}</nowiki></pre></td></tr> |
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<table><tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, -7}</nowiki></pre></td></tr> |
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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, 100]], Vassiliev[3][Knot[10, 100]]}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{4, -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[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, 100]][q, t]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4 5 1 2 1 4 2 4 |
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-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
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5 3 19 7 17 6 15 6 15 5 13 5 13 4 |
5 3 19 7 17 6 15 6 15 5 13 5 13 4 |
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Line 129: | Line 243: | ||
t 2 3 3 |
t 2 3 3 |
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-- + 2 q t + q t |
-- + 2 q t + q t |
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q</nowiki></ |
q</nowiki></code></td></tr> |
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</table> |
</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td> |
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[[Category:Knot Page]] |
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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, 100], 2][q]</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -25 3 3 4 14 13 6 32 34 7 |
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-14 + q - --- + --- + --- - --- + --- + --- - --- + --- + --- - |
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24 23 22 21 20 19 18 17 16 |
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q q q q q q q q q |
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57 51 19 77 49 37 81 33 47 66 12 45 |
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--- + --- + --- - --- + --- + --- - -- + -- + -- - -- + -- + -- - |
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15 14 13 12 11 10 9 8 7 6 5 4 |
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q q q q q q q q q q q q |
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40 5 30 2 3 4 5 |
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-- - -- + -- - 9 q + 11 q - q - 3 q + q |
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3 2 q |
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q q</nowiki></code></td></tr> |
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</table> }} |
Latest revision as of 21:06, 9 March 2007
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See the full Rolfsen Knot Table. Visit 10 100's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X18,6,19,5 X20,13,1,14 X14,7,15,8 X10,3,11,4 X16,9,17,10 X4,11,5,12 X8,15,9,16 X12,19,13,20 X2,18,3,17 |
Gauss code | 1, -10, 5, -7, 2, -1, 4, -8, 6, -5, 7, -9, 3, -4, 8, -6, 10, -2, 9, -3 |
Dowker-Thistlethwaite code | 6 10 18 14 16 4 20 8 2 12 |
Conway Notation | [3:2:2] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||
Length is 10, width is 3, Braid index is 3 |
[{3, 10}, {2, 6}, {8, 11}, {9, 7}, {10, 12}, {11, 13}, {4, 8}, {6, 9}, {5, 3}, {12, 4}, {1, 5}, {13, 2}, {7, 1}] |
[edit Notes on presentations of 10 100]
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 100"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X6271 X18,6,19,5 X20,13,1,14 X14,7,15,8 X10,3,11,4 X16,9,17,10 X4,11,5,12 X8,15,9,16 X12,19,13,20 X2,18,3,17 |
In[5]:=
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GaussCode[K]
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Out[5]=
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1, -10, 5, -7, 2, -1, 4, -8, 6, -5, 7, -9, 3, -4, 8, -6, 10, -2, 9, -3 |
In[6]:=
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DTCode[K]
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Out[6]=
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6 10 18 14 16 4 20 8 2 12 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
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ConwayNotation[K]
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Out[8]=
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[3:2:2] |
In[9]:=
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br = BR[K]
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KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
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Out[9]=
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In[10]:=
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{First[br], Crossings[br], BraidIndex[K]}
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KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
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KnotTheory::loading: Loading precomputed data in IndianaData`.
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Out[10]=
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{ 3, 10, 3 } |
In[11]:=
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Show[BraidPlot[br]]
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Out[11]=
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-Graphics- |
In[12]:=
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Show[DrawMorseLink[K]]
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KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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Out[12]=
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-Graphics- |
In[13]:=
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ap = ArcPresentation[K]
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Out[13]=
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ArcPresentation[{3, 10}, {2, 6}, {8, 11}, {9, 7}, {10, 12}, {11, 13}, {4, 8}, {6, 9}, {5, 3}, {12, 4}, {1, 5}, {13, 2}, {7, 1}] |
In[14]:=
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Draw[ap]
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Out[14]=
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-Graphics- |
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
A1 Invariants.
Weight | Invariant |
---|---|
1 | |
2 | |
3 | |
4 | |
5 | |
6 |
A2 Invariants.
Weight | Invariant |
---|---|
1,0 | |
1,1 | |
2,0 |
A3 Invariants.
Weight | Invariant |
---|---|
0,1,0 | |
1,0,0 | |
1,0,1 |
A4 Invariants.
Weight | Invariant |
---|---|
0,1,0,0 | |
1,0,0,0 |
B2 Invariants.
Weight | Invariant |
---|---|
0,1 | |
1,0 |
D4 Invariants.
Weight | Invariant |
---|---|
1,0,0,0 |
G2 Invariants.
Weight | Invariant |
---|---|
1,0 |
.
KnotTheory`
, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["10 100"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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In[5]:=
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Conway[K][z]
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Out[5]=
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In[6]:=
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Alexander[K, 2][t]
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KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
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Out[6]=
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In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 65, -4 } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, ): {}
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 100"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ , } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{} |
Vassiliev invariants
V2 and V3: | (4, -7) |
V2,1 through V6,9: |
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V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where -4 is the signature of 10 100. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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Integral Khovanov Homology
(db, data source) |
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The Coloured Jones Polynomials
2 | |
3 | |
4 | |
5 | |
6 | |
7 |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Rolfsen Knot Page master template (intermediate). See/edit the Rolfsen_Splice_Base (expert). Back to the top. |
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