10 152: Difference between revisions
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{{Rolfsen Knot Page| |
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n = 10 | |
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k = 152 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,9,-2,10,-3,1,-9,2,5,-6,-10,3,4,-8,7,-5,6,-4,8,-7/goTop.html | |
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braid_table = <table cellspacing=0 cellpadding=0 border=0> |
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{{Knot Navigation Links|ext=gif}} |
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{{Rolfsen Knot Page Header|n=10|k=152|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,9,-2,10,-3,1,-9,2,5,-6,-10,3,4,-8,7,-5,6,-4,8,-7/goTop.html}} |
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<br style="clear:both" /> |
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{{:{{PAGENAME}} Further Notes and Views}} |
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{{Knot Presentations}} |
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<center><table border=1 cellpadding=10><tr align=center valign=top> |
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<td> |
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[[Braid Representatives|Minimum Braid Representative]]: |
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<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:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.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:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr> |
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr> |
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr> |
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</table> |
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braid_crossings = 10 | |
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braid_width = 3 | |
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[[Invariants from Braid Theory|Length]] is 10, width is 3. |
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braid_index = 3 | |
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same_alexander = | |
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[[Invariants from Braid Theory|Braid index]] is 3. |
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same_jones = | |
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</td> |
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khovanov_table = <table border=1> |
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<td> |
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[[Lightly Documented Features|A Morse Link Presentation]]: |
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[[Image:{{PAGENAME}}_ML.gif]] |
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</td> |
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</tr></table></center> |
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{{3D Invariants}} |
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{{4D Invariants}} |
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{{Polynomial Invariants}} |
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=== "Similar" Knots (within the Atlas) === |
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Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]: |
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{...} |
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Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): |
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{...} |
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{{Vassiliev Invariants}} |
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{{Khovanov Homology|table=<table border=1> |
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<tr align=center> |
<tr align=center> |
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<td width=13.3333%><table cellpadding=0 cellspacing=0> |
<td width=13.3333%><table cellpadding=0 cellspacing=0> |
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<tr><td>\</td><td> </td><td>r</td></tr> |
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<tr><td> </td><td> \ </td><td> </td></tr> |
<tr><td> </td><td> \ </td><td> </td></tr> |
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<tr><td>j</td><td> </td><td>\</td></tr> |
<tr><td>j</td><td> </td><td>\</td></tr> |
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</table></td> |
</table></td> |
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<td width=6.66667%>-10</td ><td width=6.66667%>-9</td ><td width=6.66667%>-8</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=13.3333%>χ</td></tr> |
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<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td>1</td></tr> |
<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td>1</td></tr> |
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<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td>1</td></tr> |
<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td>1</td></tr> |
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<tr align=center><td>-25</td><td bgcolor=yellow> </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>-1</td></tr> |
<tr align=center><td>-25</td><td bgcolor=yellow> </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>-1</td></tr> |
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<tr align=center><td>-27</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>-27</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr> |
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</table> |
</table> | |
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coloured_jones_2 = <math> q^{-8} + q^{-11} + q^{-13} + q^{-14} -3 q^{-15} + q^{-16} +3 q^{-17} -3 q^{-18} -4 q^{-19} +5 q^{-20} + q^{-21} -9 q^{-22} +5 q^{-23} +6 q^{-24} -11 q^{-25} +4 q^{-26} +8 q^{-27} -10 q^{-28} + q^{-29} +8 q^{-30} -5 q^{-31} -3 q^{-32} +5 q^{-33} - q^{-34} -2 q^{-35} + q^{-36} </math> | |
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coloured_jones_3 = <math> q^{-12} + q^{-16} + q^{-19} + q^{-20} -3 q^{-22} + q^{-23} + q^{-24} +2 q^{-25} -2 q^{-26} -4 q^{-28} +2 q^{-30} +7 q^{-31} -6 q^{-32} -8 q^{-33} -4 q^{-34} +16 q^{-35} +6 q^{-36} -15 q^{-37} -15 q^{-38} +16 q^{-39} +23 q^{-40} -14 q^{-41} -28 q^{-42} +12 q^{-43} +33 q^{-44} -11 q^{-45} -33 q^{-46} +7 q^{-47} +36 q^{-48} -7 q^{-49} -33 q^{-50} + q^{-51} +33 q^{-52} + q^{-53} -26 q^{-54} -8 q^{-55} +21 q^{-56} +11 q^{-57} -13 q^{-58} -13 q^{-59} +5 q^{-60} +11 q^{-61} + q^{-62} -8 q^{-63} -2 q^{-64} +4 q^{-65} +2 q^{-66} - q^{-67} -2 q^{-68} + q^{-69} </math> | |
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{{Display Coloured Jones|J2=<math> q^{-8} + q^{-11} + q^{-13} + q^{-14} -3 q^{-15} + q^{-16} +3 q^{-17} -3 q^{-18} -4 q^{-19} +5 q^{-20} + q^{-21} -9 q^{-22} +5 q^{-23} +6 q^{-24} -11 q^{-25} +4 q^{-26} +8 q^{-27} -10 q^{-28} + q^{-29} +8 q^{-30} -5 q^{-31} -3 q^{-32} +5 q^{-33} - q^{-34} -2 q^{-35} + q^{-36} </math>|J3=<math> q^{-12} + q^{-16} + q^{-19} + q^{-20} -3 q^{-22} + q^{-23} + q^{-24} +2 q^{-25} -2 q^{-26} -4 q^{-28} +2 q^{-30} +7 q^{-31} -6 q^{-32} -8 q^{-33} -4 q^{-34} +16 q^{-35} +6 q^{-36} -15 q^{-37} -15 q^{-38} +16 q^{-39} +23 q^{-40} -14 q^{-41} -28 q^{-42} +12 q^{-43} +33 q^{-44} -11 q^{-45} -33 q^{-46} +7 q^{-47} +36 q^{-48} -7 q^{-49} -33 q^{-50} + q^{-51} +33 q^{-52} + q^{-53} -26 q^{-54} -8 q^{-55} +21 q^{-56} +11 q^{-57} -13 q^{-58} -13 q^{-59} +5 q^{-60} +11 q^{-61} + q^{-62} -8 q^{-63} -2 q^{-64} +4 q^{-65} +2 q^{-66} - q^{-67} -2 q^{-68} + q^{-69} </math>|J4=<math> q^{-16} + q^{-21} + q^{-25} + q^{-26} -3 q^{-29} + q^{-30} + q^{-31} +2 q^{-33} -2 q^{-34} + q^{-35} -5 q^{-37} -2 q^{-39} +5 q^{-40} +7 q^{-41} -4 q^{-42} -2 q^{-43} -11 q^{-44} -4 q^{-45} +8 q^{-46} +5 q^{-47} +16 q^{-48} -6 q^{-49} -17 q^{-50} -14 q^{-51} -7 q^{-52} +32 q^{-53} +27 q^{-54} -36 q^{-56} -46 q^{-57} +14 q^{-58} +59 q^{-59} +44 q^{-60} -31 q^{-61} -81 q^{-62} -31 q^{-63} +67 q^{-64} +89 q^{-65} -9 q^{-66} -98 q^{-67} -71 q^{-68} +63 q^{-69} +113 q^{-70} +9 q^{-71} -99 q^{-72} -92 q^{-73} +57 q^{-74} +121 q^{-75} +17 q^{-76} -93 q^{-77} -100 q^{-78} +48 q^{-79} +117 q^{-80} +27 q^{-81} -76 q^{-82} -103 q^{-83} +25 q^{-84} +99 q^{-85} +43 q^{-86} -38 q^{-87} -92 q^{-88} -11 q^{-89} +55 q^{-90} +49 q^{-91} +12 q^{-92} -56 q^{-93} -29 q^{-94} +5 q^{-95} +25 q^{-96} +32 q^{-97} -13 q^{-98} -15 q^{-99} -14 q^{-100} -2 q^{-101} +19 q^{-102} +2 q^{-103} -6 q^{-105} -6 q^{-106} +5 q^{-107} + q^{-108} +2 q^{-109} - q^{-110} -2 q^{-111} + q^{-112} </math>|J5=<math> q^{-20} + q^{-26} + q^{-31} + q^{-32} -3 q^{-36} + q^{-37} + q^{-38} +2 q^{-41} -2 q^{-42} + q^{-43} + q^{-44} - q^{-45} -5 q^{-46} -2 q^{-48} + q^{-49} +5 q^{-50} +6 q^{-51} -4 q^{-52} + q^{-53} -5 q^{-54} -8 q^{-55} -4 q^{-56} +4 q^{-57} -3 q^{-58} +12 q^{-59} +13 q^{-60} + q^{-61} -4 q^{-62} -12 q^{-63} -26 q^{-64} -9 q^{-65} +13 q^{-66} +22 q^{-67} +35 q^{-68} +20 q^{-69} -23 q^{-70} -42 q^{-71} -45 q^{-72} -24 q^{-73} +39 q^{-74} +81 q^{-75} +57 q^{-76} +5 q^{-77} -69 q^{-78} -126 q^{-79} -63 q^{-80} +55 q^{-81} +142 q^{-82} +138 q^{-83} +17 q^{-84} -161 q^{-85} -210 q^{-86} -81 q^{-87} +132 q^{-88} +261 q^{-89} +169 q^{-90} -97 q^{-91} -296 q^{-92} -244 q^{-93} +52 q^{-94} +312 q^{-95} +302 q^{-96} - q^{-97} -320 q^{-98} -346 q^{-99} -34 q^{-100} +318 q^{-101} +371 q^{-102} +65 q^{-103} -316 q^{-104} -390 q^{-105} -77 q^{-106} +308 q^{-107} +394 q^{-108} +96 q^{-109} -306 q^{-110} -402 q^{-111} -97 q^{-112} +294 q^{-113} +396 q^{-114} +119 q^{-115} -282 q^{-116} -401 q^{-117} -127 q^{-118} +252 q^{-119} +385 q^{-120} +165 q^{-121} -211 q^{-122} -371 q^{-123} -186 q^{-124} +145 q^{-125} +326 q^{-126} +218 q^{-127} -68 q^{-128} -268 q^{-129} -221 q^{-130} -10 q^{-131} +181 q^{-132} +208 q^{-133} +66 q^{-134} -93 q^{-135} -159 q^{-136} -99 q^{-137} +19 q^{-138} +100 q^{-139} +93 q^{-140} +25 q^{-141} -39 q^{-142} -66 q^{-143} -43 q^{-144} + q^{-145} +36 q^{-146} +34 q^{-147} +14 q^{-148} -5 q^{-149} -23 q^{-150} -18 q^{-151} - q^{-152} +9 q^{-153} +9 q^{-154} +6 q^{-155} -8 q^{-157} -4 q^{-158} + q^{-159} +2 q^{-160} + q^{-161} +2 q^{-162} - q^{-163} -2 q^{-164} + q^{-165} </math>|J6=<math> q^{-24} + q^{-31} + q^{-37} + q^{-38} -3 q^{-43} + q^{-44} + q^{-45} +2 q^{-49} -2 q^{-50} + q^{-51} + q^{-52} - q^{-54} -5 q^{-55} -2 q^{-57} + q^{-58} + q^{-59} +4 q^{-60} +6 q^{-61} -4 q^{-62} + q^{-63} -2 q^{-64} -2 q^{-65} -8 q^{-66} -5 q^{-67} +4 q^{-68} -6 q^{-69} +4 q^{-70} +9 q^{-71} +16 q^{-72} + q^{-73} - q^{-74} + q^{-75} -22 q^{-76} -20 q^{-77} -13 q^{-78} +8 q^{-79} +6 q^{-80} +22 q^{-81} +40 q^{-82} +16 q^{-83} -2 q^{-84} -20 q^{-85} -32 q^{-86} -56 q^{-87} -39 q^{-88} +14 q^{-89} +39 q^{-90} +68 q^{-91} +81 q^{-92} +51 q^{-93} -28 q^{-94} -105 q^{-95} -116 q^{-96} -110 q^{-97} -30 q^{-98} +101 q^{-99} +195 q^{-100} +195 q^{-101} +76 q^{-102} -68 q^{-103} -249 q^{-104} -307 q^{-105} -190 q^{-106} +67 q^{-107} +318 q^{-108} +404 q^{-109} +315 q^{-110} -35 q^{-111} -395 q^{-112} -586 q^{-113} -404 q^{-114} +49 q^{-115} +496 q^{-116} +744 q^{-117} +497 q^{-118} -78 q^{-119} -722 q^{-120} -888 q^{-121} -492 q^{-122} +232 q^{-123} +912 q^{-124} +1003 q^{-125} +448 q^{-126} -555 q^{-127} -1135 q^{-128} -979 q^{-129} -170 q^{-130} +837 q^{-131} +1289 q^{-132} +881 q^{-133} -299 q^{-134} -1175 q^{-135} -1257 q^{-136} -469 q^{-137} +699 q^{-138} +1392 q^{-139} +1113 q^{-140} -127 q^{-141} -1144 q^{-142} -1364 q^{-143} -608 q^{-144} +607 q^{-145} +1409 q^{-146} +1200 q^{-147} -51 q^{-148} -1115 q^{-149} -1390 q^{-150} -657 q^{-151} +557 q^{-152} +1403 q^{-153} +1233 q^{-154} -4 q^{-155} -1082 q^{-156} -1400 q^{-157} -704 q^{-158} +483 q^{-159} +1371 q^{-160} +1274 q^{-161} +108 q^{-162} -973 q^{-163} -1385 q^{-164} -818 q^{-165} +275 q^{-166} +1223 q^{-167} +1306 q^{-168} +361 q^{-169} -659 q^{-170} -1231 q^{-171} -956 q^{-172} -125 q^{-173} +819 q^{-174} +1172 q^{-175} +648 q^{-176} -127 q^{-177} -785 q^{-178} -893 q^{-179} -516 q^{-180} +213 q^{-181} +717 q^{-182} +663 q^{-183} +314 q^{-184} -179 q^{-185} -486 q^{-186} -548 q^{-187} -211 q^{-188} +156 q^{-189} +327 q^{-190} +341 q^{-191} +168 q^{-192} -39 q^{-193} -252 q^{-194} -214 q^{-195} -105 q^{-196} +9 q^{-197} +108 q^{-198} +137 q^{-199} +108 q^{-200} -20 q^{-201} -48 q^{-202} -69 q^{-203} -55 q^{-204} -24 q^{-205} +19 q^{-206} +56 q^{-207} +18 q^{-208} +17 q^{-209} -4 q^{-210} -15 q^{-211} -24 q^{-212} -12 q^{-213} +11 q^{-214} +2 q^{-215} +10 q^{-216} +5 q^{-217} +3 q^{-218} -8 q^{-219} -6 q^{-220} +3 q^{-221} -2 q^{-222} +2 q^{-223} + q^{-224} +2 q^{-225} - q^{-226} -2 q^{-227} + q^{-228} </math>|J7=<math> q^{-28} + q^{-36} + q^{-43} + q^{-44} -3 q^{-50} + q^{-51} + q^{-52} +2 q^{-57} -2 q^{-58} + q^{-59} + q^{-60} - q^{-63} -5 q^{-64} -2 q^{-66} + q^{-67} + q^{-68} +4 q^{-70} +6 q^{-71} -4 q^{-72} + q^{-73} -2 q^{-74} + q^{-75} -2 q^{-76} -9 q^{-77} -5 q^{-78} +4 q^{-79} -6 q^{-80} + q^{-81} + q^{-82} +12 q^{-83} +16 q^{-84} - q^{-86} +5 q^{-87} -9 q^{-88} -16 q^{-89} -23 q^{-90} -10 q^{-91} +7 q^{-92} -3 q^{-93} +6 q^{-94} +28 q^{-95} +32 q^{-96} +22 q^{-97} - q^{-98} -2 q^{-99} -7 q^{-100} -44 q^{-101} -59 q^{-102} -36 q^{-103} -7 q^{-104} +15 q^{-105} +29 q^{-106} +77 q^{-107} +99 q^{-108} +53 q^{-109} +3 q^{-110} -46 q^{-111} -84 q^{-112} -129 q^{-113} -144 q^{-114} -65 q^{-115} +45 q^{-116} +110 q^{-117} +189 q^{-118} +211 q^{-119} +169 q^{-120} +30 q^{-121} -166 q^{-122} -273 q^{-123} -323 q^{-124} -298 q^{-125} -103 q^{-126} +163 q^{-127} +416 q^{-128} +536 q^{-129} +427 q^{-130} +195 q^{-131} -189 q^{-132} -625 q^{-133} -797 q^{-134} -678 q^{-135} -229 q^{-136} +371 q^{-137} +877 q^{-138} +1151 q^{-139} +938 q^{-140} +178 q^{-141} -701 q^{-142} -1391 q^{-143} -1538 q^{-144} -983 q^{-145} +44 q^{-146} +1281 q^{-147} +2058 q^{-148} +1854 q^{-149} +789 q^{-150} -788 q^{-151} -2157 q^{-152} -2587 q^{-153} -1840 q^{-154} -40 q^{-155} +1987 q^{-156} +3088 q^{-157} +2785 q^{-158} +1004 q^{-159} -1458 q^{-160} -3281 q^{-161} -3597 q^{-162} -2002 q^{-163} +771 q^{-164} +3238 q^{-165} +4165 q^{-166} +2893 q^{-167} -55 q^{-168} -3005 q^{-169} -4507 q^{-170} -3604 q^{-171} -631 q^{-172} +2701 q^{-173} +4700 q^{-174} +4119 q^{-175} +1167 q^{-176} -2399 q^{-177} -4744 q^{-178} -4463 q^{-179} -1586 q^{-180} +2151 q^{-181} +4747 q^{-182} +4671 q^{-183} +1843 q^{-184} -1956 q^{-185} -4706 q^{-186} -4788 q^{-187} -2022 q^{-188} +1839 q^{-189} +4684 q^{-190} +4835 q^{-191} +2101 q^{-192} -1753 q^{-193} -4634 q^{-194} -4872 q^{-195} -2178 q^{-196} +1713 q^{-197} +4635 q^{-198} +4881 q^{-199} +2196 q^{-200} -1659 q^{-201} -4587 q^{-202} -4916 q^{-203} -2289 q^{-204} +1603 q^{-205} +4587 q^{-206} +4946 q^{-207} +2363 q^{-208} -1472 q^{-209} -4484 q^{-210} -5002 q^{-211} -2573 q^{-212} +1252 q^{-213} +4360 q^{-214} +5033 q^{-215} +2803 q^{-216} -873 q^{-217} -4023 q^{-218} -5009 q^{-219} -3154 q^{-220} +317 q^{-221} +3533 q^{-222} +4833 q^{-223} +3453 q^{-224} +395 q^{-225} -2747 q^{-226} -4413 q^{-227} -3685 q^{-228} -1165 q^{-229} +1773 q^{-230} +3710 q^{-231} +3631 q^{-232} +1834 q^{-233} -666 q^{-234} -2738 q^{-235} -3262 q^{-236} -2240 q^{-237} -313 q^{-238} +1613 q^{-239} +2547 q^{-240} +2262 q^{-241} +1034 q^{-242} -566 q^{-243} -1667 q^{-244} -1884 q^{-245} -1326 q^{-246} -225 q^{-247} +767 q^{-248} +1290 q^{-249} +1243 q^{-250} +624 q^{-251} -99 q^{-252} -652 q^{-253} -882 q^{-254} -679 q^{-255} -271 q^{-256} +146 q^{-257} +479 q^{-258} +514 q^{-259} +356 q^{-260} +114 q^{-261} -158 q^{-262} -258 q^{-263} -272 q^{-264} -201 q^{-265} -31 q^{-266} +93 q^{-267} +150 q^{-268} +147 q^{-269} +67 q^{-270} +20 q^{-271} -31 q^{-272} -93 q^{-273} -68 q^{-274} -39 q^{-275} +32 q^{-277} +23 q^{-278} +32 q^{-279} +28 q^{-280} -4 q^{-281} -15 q^{-282} -20 q^{-283} -15 q^{-284} +3 q^{-285} -3 q^{-286} +4 q^{-287} +12 q^{-288} +5 q^{-289} +2 q^{-290} -5 q^{-291} -6 q^{-292} + q^{-293} -2 q^{-295} +2 q^{-296} + q^{-297} +2 q^{-298} - q^{-299} -2 q^{-300} + q^{-301} </math>}} |
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coloured_jones_4 = <math> q^{-16} + q^{-21} + q^{-25} + q^{-26} -3 q^{-29} + q^{-30} + q^{-31} +2 q^{-33} -2 q^{-34} + q^{-35} -5 q^{-37} -2 q^{-39} +5 q^{-40} +7 q^{-41} -4 q^{-42} -2 q^{-43} -11 q^{-44} -4 q^{-45} +8 q^{-46} +5 q^{-47} +16 q^{-48} -6 q^{-49} -17 q^{-50} -14 q^{-51} -7 q^{-52} +32 q^{-53} +27 q^{-54} -36 q^{-56} -46 q^{-57} +14 q^{-58} +59 q^{-59} +44 q^{-60} -31 q^{-61} -81 q^{-62} -31 q^{-63} +67 q^{-64} +89 q^{-65} -9 q^{-66} -98 q^{-67} -71 q^{-68} +63 q^{-69} +113 q^{-70} +9 q^{-71} -99 q^{-72} -92 q^{-73} +57 q^{-74} +121 q^{-75} +17 q^{-76} -93 q^{-77} -100 q^{-78} +48 q^{-79} +117 q^{-80} +27 q^{-81} -76 q^{-82} -103 q^{-83} +25 q^{-84} +99 q^{-85} +43 q^{-86} -38 q^{-87} -92 q^{-88} -11 q^{-89} +55 q^{-90} +49 q^{-91} +12 q^{-92} -56 q^{-93} -29 q^{-94} +5 q^{-95} +25 q^{-96} +32 q^{-97} -13 q^{-98} -15 q^{-99} -14 q^{-100} -2 q^{-101} +19 q^{-102} +2 q^{-103} -6 q^{-105} -6 q^{-106} +5 q^{-107} + q^{-108} +2 q^{-109} - q^{-110} -2 q^{-111} + q^{-112} </math> | |
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coloured_jones_5 = <math> q^{-20} + q^{-26} + q^{-31} + q^{-32} -3 q^{-36} + q^{-37} + q^{-38} +2 q^{-41} -2 q^{-42} + q^{-43} + q^{-44} - q^{-45} -5 q^{-46} -2 q^{-48} + q^{-49} +5 q^{-50} +6 q^{-51} -4 q^{-52} + q^{-53} -5 q^{-54} -8 q^{-55} -4 q^{-56} +4 q^{-57} -3 q^{-58} +12 q^{-59} +13 q^{-60} + q^{-61} -4 q^{-62} -12 q^{-63} -26 q^{-64} -9 q^{-65} +13 q^{-66} +22 q^{-67} +35 q^{-68} +20 q^{-69} -23 q^{-70} -42 q^{-71} -45 q^{-72} -24 q^{-73} +39 q^{-74} +81 q^{-75} +57 q^{-76} +5 q^{-77} -69 q^{-78} -126 q^{-79} -63 q^{-80} +55 q^{-81} +142 q^{-82} +138 q^{-83} +17 q^{-84} -161 q^{-85} -210 q^{-86} -81 q^{-87} +132 q^{-88} +261 q^{-89} +169 q^{-90} -97 q^{-91} -296 q^{-92} -244 q^{-93} +52 q^{-94} +312 q^{-95} +302 q^{-96} - q^{-97} -320 q^{-98} -346 q^{-99} -34 q^{-100} +318 q^{-101} +371 q^{-102} +65 q^{-103} -316 q^{-104} -390 q^{-105} -77 q^{-106} +308 q^{-107} +394 q^{-108} +96 q^{-109} -306 q^{-110} -402 q^{-111} -97 q^{-112} +294 q^{-113} +396 q^{-114} +119 q^{-115} -282 q^{-116} -401 q^{-117} -127 q^{-118} +252 q^{-119} +385 q^{-120} +165 q^{-121} -211 q^{-122} -371 q^{-123} -186 q^{-124} +145 q^{-125} +326 q^{-126} +218 q^{-127} -68 q^{-128} -268 q^{-129} -221 q^{-130} -10 q^{-131} +181 q^{-132} +208 q^{-133} +66 q^{-134} -93 q^{-135} -159 q^{-136} -99 q^{-137} +19 q^{-138} +100 q^{-139} +93 q^{-140} +25 q^{-141} -39 q^{-142} -66 q^{-143} -43 q^{-144} + q^{-145} +36 q^{-146} +34 q^{-147} +14 q^{-148} -5 q^{-149} -23 q^{-150} -18 q^{-151} - q^{-152} +9 q^{-153} +9 q^{-154} +6 q^{-155} -8 q^{-157} -4 q^{-158} + q^{-159} +2 q^{-160} + q^{-161} +2 q^{-162} - q^{-163} -2 q^{-164} + q^{-165} </math> | |
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{{Computer Talk Header}} |
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coloured_jones_6 = <math> q^{-24} + q^{-31} + q^{-37} + q^{-38} -3 q^{-43} + q^{-44} + q^{-45} +2 q^{-49} -2 q^{-50} + q^{-51} + q^{-52} - q^{-54} -5 q^{-55} -2 q^{-57} + q^{-58} + q^{-59} +4 q^{-60} +6 q^{-61} -4 q^{-62} + q^{-63} -2 q^{-64} -2 q^{-65} -8 q^{-66} -5 q^{-67} +4 q^{-68} -6 q^{-69} +4 q^{-70} +9 q^{-71} +16 q^{-72} + q^{-73} - q^{-74} + q^{-75} -22 q^{-76} -20 q^{-77} -13 q^{-78} +8 q^{-79} +6 q^{-80} +22 q^{-81} +40 q^{-82} +16 q^{-83} -2 q^{-84} -20 q^{-85} -32 q^{-86} -56 q^{-87} -39 q^{-88} +14 q^{-89} +39 q^{-90} +68 q^{-91} +81 q^{-92} +51 q^{-93} -28 q^{-94} -105 q^{-95} -116 q^{-96} -110 q^{-97} -30 q^{-98} +101 q^{-99} +195 q^{-100} +195 q^{-101} +76 q^{-102} -68 q^{-103} -249 q^{-104} -307 q^{-105} -190 q^{-106} +67 q^{-107} +318 q^{-108} +404 q^{-109} +315 q^{-110} -35 q^{-111} -395 q^{-112} -586 q^{-113} -404 q^{-114} +49 q^{-115} +496 q^{-116} +744 q^{-117} +497 q^{-118} -78 q^{-119} -722 q^{-120} -888 q^{-121} -492 q^{-122} +232 q^{-123} +912 q^{-124} +1003 q^{-125} +448 q^{-126} -555 q^{-127} -1135 q^{-128} -979 q^{-129} -170 q^{-130} +837 q^{-131} +1289 q^{-132} +881 q^{-133} -299 q^{-134} -1175 q^{-135} -1257 q^{-136} -469 q^{-137} +699 q^{-138} +1392 q^{-139} +1113 q^{-140} -127 q^{-141} -1144 q^{-142} -1364 q^{-143} -608 q^{-144} +607 q^{-145} +1409 q^{-146} +1200 q^{-147} -51 q^{-148} -1115 q^{-149} -1390 q^{-150} -657 q^{-151} +557 q^{-152} +1403 q^{-153} +1233 q^{-154} -4 q^{-155} -1082 q^{-156} -1400 q^{-157} -704 q^{-158} +483 q^{-159} +1371 q^{-160} +1274 q^{-161} +108 q^{-162} -973 q^{-163} -1385 q^{-164} -818 q^{-165} +275 q^{-166} +1223 q^{-167} +1306 q^{-168} +361 q^{-169} -659 q^{-170} -1231 q^{-171} -956 q^{-172} -125 q^{-173} +819 q^{-174} +1172 q^{-175} +648 q^{-176} -127 q^{-177} -785 q^{-178} -893 q^{-179} -516 q^{-180} +213 q^{-181} +717 q^{-182} +663 q^{-183} +314 q^{-184} -179 q^{-185} -486 q^{-186} -548 q^{-187} -211 q^{-188} +156 q^{-189} +327 q^{-190} +341 q^{-191} +168 q^{-192} -39 q^{-193} -252 q^{-194} -214 q^{-195} -105 q^{-196} +9 q^{-197} +108 q^{-198} +137 q^{-199} +108 q^{-200} -20 q^{-201} -48 q^{-202} -69 q^{-203} -55 q^{-204} -24 q^{-205} +19 q^{-206} +56 q^{-207} +18 q^{-208} +17 q^{-209} -4 q^{-210} -15 q^{-211} -24 q^{-212} -12 q^{-213} +11 q^{-214} +2 q^{-215} +10 q^{-216} +5 q^{-217} +3 q^{-218} -8 q^{-219} -6 q^{-220} +3 q^{-221} -2 q^{-222} +2 q^{-223} + q^{-224} +2 q^{-225} - q^{-226} -2 q^{-227} + q^{-228} </math> | |
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coloured_jones_7 = <math> q^{-28} + q^{-36} + q^{-43} + q^{-44} -3 q^{-50} + q^{-51} + q^{-52} +2 q^{-57} -2 q^{-58} + q^{-59} + q^{-60} - q^{-63} -5 q^{-64} -2 q^{-66} + q^{-67} + q^{-68} +4 q^{-70} +6 q^{-71} -4 q^{-72} + q^{-73} -2 q^{-74} + q^{-75} -2 q^{-76} -9 q^{-77} -5 q^{-78} +4 q^{-79} -6 q^{-80} + q^{-81} + q^{-82} +12 q^{-83} +16 q^{-84} - q^{-86} +5 q^{-87} -9 q^{-88} -16 q^{-89} -23 q^{-90} -10 q^{-91} +7 q^{-92} -3 q^{-93} +6 q^{-94} +28 q^{-95} +32 q^{-96} +22 q^{-97} - q^{-98} -2 q^{-99} -7 q^{-100} -44 q^{-101} -59 q^{-102} -36 q^{-103} -7 q^{-104} +15 q^{-105} +29 q^{-106} +77 q^{-107} +99 q^{-108} +53 q^{-109} +3 q^{-110} -46 q^{-111} -84 q^{-112} -129 q^{-113} -144 q^{-114} -65 q^{-115} +45 q^{-116} +110 q^{-117} +189 q^{-118} +211 q^{-119} +169 q^{-120} +30 q^{-121} -166 q^{-122} -273 q^{-123} -323 q^{-124} -298 q^{-125} -103 q^{-126} +163 q^{-127} +416 q^{-128} +536 q^{-129} +427 q^{-130} +195 q^{-131} -189 q^{-132} -625 q^{-133} -797 q^{-134} -678 q^{-135} -229 q^{-136} +371 q^{-137} +877 q^{-138} +1151 q^{-139} +938 q^{-140} +178 q^{-141} -701 q^{-142} -1391 q^{-143} -1538 q^{-144} -983 q^{-145} +44 q^{-146} +1281 q^{-147} +2058 q^{-148} +1854 q^{-149} +789 q^{-150} -788 q^{-151} -2157 q^{-152} -2587 q^{-153} -1840 q^{-154} -40 q^{-155} +1987 q^{-156} +3088 q^{-157} +2785 q^{-158} +1004 q^{-159} -1458 q^{-160} -3281 q^{-161} -3597 q^{-162} -2002 q^{-163} +771 q^{-164} +3238 q^{-165} +4165 q^{-166} +2893 q^{-167} -55 q^{-168} -3005 q^{-169} -4507 q^{-170} -3604 q^{-171} -631 q^{-172} +2701 q^{-173} +4700 q^{-174} +4119 q^{-175} +1167 q^{-176} -2399 q^{-177} -4744 q^{-178} -4463 q^{-179} -1586 q^{-180} +2151 q^{-181} +4747 q^{-182} +4671 q^{-183} +1843 q^{-184} -1956 q^{-185} -4706 q^{-186} -4788 q^{-187} -2022 q^{-188} +1839 q^{-189} +4684 q^{-190} +4835 q^{-191} +2101 q^{-192} -1753 q^{-193} -4634 q^{-194} -4872 q^{-195} -2178 q^{-196} +1713 q^{-197} +4635 q^{-198} +4881 q^{-199} +2196 q^{-200} -1659 q^{-201} -4587 q^{-202} -4916 q^{-203} -2289 q^{-204} +1603 q^{-205} +4587 q^{-206} +4946 q^{-207} +2363 q^{-208} -1472 q^{-209} -4484 q^{-210} -5002 q^{-211} -2573 q^{-212} +1252 q^{-213} +4360 q^{-214} +5033 q^{-215} +2803 q^{-216} -873 q^{-217} -4023 q^{-218} -5009 q^{-219} -3154 q^{-220} +317 q^{-221} +3533 q^{-222} +4833 q^{-223} +3453 q^{-224} +395 q^{-225} -2747 q^{-226} -4413 q^{-227} -3685 q^{-228} -1165 q^{-229} +1773 q^{-230} +3710 q^{-231} +3631 q^{-232} +1834 q^{-233} -666 q^{-234} -2738 q^{-235} -3262 q^{-236} -2240 q^{-237} -313 q^{-238} +1613 q^{-239} +2547 q^{-240} +2262 q^{-241} +1034 q^{-242} -566 q^{-243} -1667 q^{-244} -1884 q^{-245} -1326 q^{-246} -225 q^{-247} +767 q^{-248} +1290 q^{-249} +1243 q^{-250} +624 q^{-251} -99 q^{-252} -652 q^{-253} -882 q^{-254} -679 q^{-255} -271 q^{-256} +146 q^{-257} +479 q^{-258} +514 q^{-259} +356 q^{-260} +114 q^{-261} -158 q^{-262} -258 q^{-263} -272 q^{-264} -201 q^{-265} -31 q^{-266} +93 q^{-267} +150 q^{-268} +147 q^{-269} +67 q^{-270} +20 q^{-271} -31 q^{-272} -93 q^{-273} -68 q^{-274} -39 q^{-275} +32 q^{-277} +23 q^{-278} +32 q^{-279} +28 q^{-280} -4 q^{-281} -15 q^{-282} -20 q^{-283} -15 q^{-284} +3 q^{-285} -3 q^{-286} +4 q^{-287} +12 q^{-288} +5 q^{-289} +2 q^{-290} -5 q^{-291} -6 q^{-292} + q^{-293} -2 q^{-295} +2 q^{-296} + q^{-297} +2 q^{-298} - q^{-299} -2 q^{-300} + q^{-301} </math> | |
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computer_talk = |
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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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<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 colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></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>PD[Knot[10, 152]]</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[2]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 6, 2, 7], X[3, 8, 4, 9], X[5, 12, 6, 13], X[18, 13, 19, 14], |
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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, 152]]</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[1, 6, 2, 7], X[3, 8, 4, 9], X[5, 12, 6, 13], X[18, 13, 19, 14], |
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X[16, 9, 17, 10], X[10, 17, 11, 18], X[20, 15, 1, 16], |
X[16, 9, 17, 10], X[10, 17, 11, 18], X[20, 15, 1, 16], |
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X[14, 19, 15, 20], X[7, 2, 8, 3], X[11, 4, 12, 5]]</nowiki></ |
X[14, 19, 15, 20], X[7, 2, 8, 3], X[11, 4, 12, 5]]</nowiki></code></td></tr> |
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</table> |
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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>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 152]]</nowiki></pre></td></tr> |
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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, 152]]</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, 9, -2, 10, -3, 1, -9, 2, 5, -6, -10, 3, 4, -8, 7, -5, 6, |
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-4, 8, -7]</nowiki></ |
-4, 8, -7]</nowiki></code></td></tr> |
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</table> |
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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>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>DTCode[Knot[10, 152]]</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, 152]]</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>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>br = BR[Knot[10, 152]]</nowiki></pre></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, 8, 12, 2, -16, 4, -18, -20, -10, -14]</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[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{3, 10}</nowiki></pre></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, 152]]</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[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>3</nowiki></pre></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, -2, -1, -1, -2, -2, -2}]</nowiki></code></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 152]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_152_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
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</table> |
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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>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 152]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></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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<tr align=left> |
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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>alex = Alexander[Knot[10, 152]][t]</nowiki></pre></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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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 152]]</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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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 152]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:10_152_ML.gif]]</td></tr><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 152]]&) /@ { |
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SymmetryType, UnknottingNumber, ThreeGenus, |
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BridgeIndex, SuperBridgeIndex, NakanishiIndex |
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}</nowiki></code></td></tr> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 4, 4, 3, NotAvailable, 1}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 152]][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 -3 -2 4 2 3 4 |
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-5 + t - t - t + - + 4 t - t - t + t |
-5 + t - t - t + - + 4 t - t - t + t |
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t</nowiki></ |
t</nowiki></code></td></tr> |
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</table> |
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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>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 152]][z]</nowiki></pre></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 152]][z]</nowiki></code></td></tr> |
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<tr align=left> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6 8 |
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1 + 7 z + 13 z + 7 z + 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[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[10, 152]], KnotSignature[Knot[10, 152]]}</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>{11, -6}</nowiki></pre></td></tr> |
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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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<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> -13 2 2 3 2 2 -7 -6 -4 |
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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, 152]}</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, 152]], KnotSignature[Knot[10, 152]]}</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[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>{11, -6}</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[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, 152]][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[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> -13 2 2 3 2 2 -7 -6 -4 |
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q - --- + --- - --- + -- - -- + q + q + q |
q - --- + --- - --- + -- - -- + q + q + q |
||
12 11 10 9 8 |
12 11 10 9 8 |
||
q q q q q</nowiki></ |
q q q q q</nowiki></code></td></tr> |
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</table> |
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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>In[15]:=</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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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr> |
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<tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 152]][q]</nowiki></pre></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 152]}</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, 152]][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> 2 -34 3 2 3 -24 2 3 2 -16 -14 |
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--- - q - --- - --- - --- + q + --- + --- + --- + q + q |
--- - q - --- - --- - --- + q + --- + --- + --- + q + q |
||
40 32 30 28 22 20 18 |
40 32 30 28 22 20 18 |
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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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<table><tr align=left> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 152]][a, z]</nowiki></pre></td></tr> |
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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, 152]][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[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> 8 10 12 8 2 10 2 12 2 8 4 |
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8 a - 10 a + 3 a + 22 a z - 17 a z + 2 a z + 21 a z - |
8 a - 10 a + 3 a + 22 a z - 17 a z + 2 a z + 21 a z - |
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10 4 8 6 10 6 8 8 |
10 4 8 6 10 6 8 8 |
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8 a z + 8 a z - a z + a z</nowiki></ |
8 a z + 8 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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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 152]][a, z]</nowiki></pre></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 152]][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> 8 10 12 9 11 13 15 |
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8 a + 10 a + 3 a - 10 a z - 11 a z + a z + 2 a z - |
8 a + 10 a + 3 a - 10 a z - 11 a z + a z + 2 a z - |
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Line 164: | Line 205: | ||
8 6 10 6 14 6 9 7 11 7 8 8 10 8 |
8 6 10 6 14 6 9 7 11 7 8 8 10 8 |
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8 a z - 9 a z + a z + a z + a z + a z + a z</nowiki></ |
8 a z - 9 a z + a z + a z + 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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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 152]], Vassiliev[3][Knot[10, 152]]}</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, 152]], Vassiliev[3][Knot[10, 152]]}</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>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 152]][q, t]</nowiki></pre></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{7, -15}</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, 152]][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> -9 -7 1 1 1 1 1 2 |
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q + q + ------- + ------ + ------ + ------ + ------ + ------ + |
q + q + ------- + ------ + ------ + ------ + ------ + ------ + |
||
27 10 25 9 23 9 23 8 21 8 21 7 |
27 10 25 9 23 9 23 8 21 8 21 7 |
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Line 183: | Line 232: | ||
------ + ------ + ------ |
------ + ------ + ------ |
||
13 4 15 3 11 2 |
13 4 15 3 11 2 |
||
q t q t q t</nowiki></ |
q t q t q t</nowiki></code></td></tr> |
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</table> |
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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>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 152], 2][q]</nowiki></pre></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 152], 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> -36 2 -34 5 3 5 8 -29 10 8 4 |
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q - --- - q + --- - --- - --- + --- + q - --- + --- + --- - |
q - --- - q + --- - --- - --- + --- + q - --- + --- + --- - |
||
35 33 32 31 30 28 27 26 |
35 33 32 31 30 28 27 26 |
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Line 197: | Line 250: | ||
-14 -13 -11 -8 |
-14 -13 -11 -8 |
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q + q + q + q</nowiki></ |
q + q + q + q</nowiki></code></td></tr> |
||
</table> }} |
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</table> |
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{| width=100% |
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|align=left|See/edit the [[Rolfsen_Splice_Template]]. |
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Back to the [[#top|top]]. |
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|align=right|{{Knot Navigation Links|ext=gif}} |
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|} |
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[[Category:Knot Page]] |
Latest revision as of 17:03, 1 September 2005
|
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(KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 152's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X1627 X3849 X5,12,6,13 X18,13,19,14 X16,9,17,10 X10,17,11,18 X20,15,1,16 X14,19,15,20 X7283 X11,4,12,5 |
Gauss code | -1, 9, -2, 10, -3, 1, -9, 2, 5, -6, -10, 3, 4, -8, 7, -5, 6, -4, 8, -7 |
Dowker-Thistlethwaite code | 6 8 12 2 -16 4 -18 -20 -10 -14 |
Conway Notation | [(3,2)-(3,2)] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||
Length is 10, width is 3, Braid index is 3 |
[{7, 2}, {1, 3}, {2, 5}, {9, 6}, {3, 7}, {4, 8}, {5, 9}, {6, 10}, {8, 1}, {10, 4}] |
[edit Notes on presentations of 10 152]
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]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
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K = Knot["10 152"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1627 X3849 X5,12,6,13 X18,13,19,14 X16,9,17,10 X10,17,11,18 X20,15,1,16 X14,19,15,20 X7283 X11,4,12,5 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 9, -2, 10, -3, 1, -9, 2, 5, -6, -10, 3, 4, -8, 7, -5, 6, -4, 8, -7 |
In[6]:=
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DTCode[K]
|
Out[6]=
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6 8 12 2 -16 4 -18 -20 -10 -14 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
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ConwayNotation[K]
|
Out[8]=
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[(3,2)-(3,2)] |
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.
|
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[{7, 2}, {1, 3}, {2, 5}, {9, 6}, {3, 7}, {4, 8}, {5, 9}, {6, 10}, {8, 1}, {10, 4}] |
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 | |
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]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["10 152"];
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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.
|
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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{ 11, -6 } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
|
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
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`.
|
Out[10]=
|
"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]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["10 152"];
|
In[4]:=
|
{A = Alexander[K][t], J = Jones[K][q]}
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
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]=
|
{} |
Vassiliev invariants
V2 and V3: | (7, -15) |
V2,1 through V6,9: |
|
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 -6 is the signature of 10 152. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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Integral Khovanov Homology
(db, data source) |
|
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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