10 41: Difference between revisions
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{{Rolfsen Knot Page| |
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n = 10 | |
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k = 41 | |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,8,-9,7,-5,3,-4,2,-7,10,-6,9,-8,6,-10,5/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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<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
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{| align=left |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr> |
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|[[Image:{{PAGENAME}}.gif]] |
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr> |
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|{{Rolfsen Knot Site Links|n=10|k=41|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,8,-9,7,-5,3,-4,2,-7,10,-6,9,-8,6,-10,5/goTop.html}} |
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</table> | |
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|{{:{{PAGENAME}} Quick Notes}} |
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braid_crossings = 10 | |
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braid_width = 5 | |
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braid_index = 5 | |
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<br style="clear:both" /> |
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same_alexander = [[K11n5]], | |
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same_jones = [[10_94]], | |
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{{:{{PAGENAME}} Further Notes and Views}} |
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khovanov_table = <table border=1> |
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{{Knot Presentations}} |
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{{3D Invariants}} |
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{{4D Invariants}} |
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{{Polynomial Invariants}} |
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{{Vassiliev Invariants}} |
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===[[Khovanov Homology]]=== |
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The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>. |
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<center><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%>-6</td ><td width=6.66667%>-5</td ><td width=6.66667%>-4</td ><td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=13.3333%>χ</td></tr> |
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<tr align=center><td>7</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>7</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>5</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>5</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>-13</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> |
<tr align=center><td>-13</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>-15</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>-15</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^{10}-3 q^9+11 q^7-13 q^6-10 q^5+37 q^4-22 q^3-37 q^2+71 q-19-74 q^{-1} +97 q^{-2} -6 q^{-3} -104 q^{-4} +103 q^{-5} +12 q^{-6} -110 q^{-7} +85 q^{-8} +22 q^{-9} -86 q^{-10} +53 q^{-11} +18 q^{-12} -47 q^{-13} +24 q^{-14} +8 q^{-15} -17 q^{-16} +7 q^{-17} +2 q^{-18} -3 q^{-19} + q^{-20} </math> | |
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coloured_jones_3 = <math>q^{21}-3 q^{20}+5 q^{18}+6 q^{17}-13 q^{16}-17 q^{15}+20 q^{14}+39 q^{13}-22 q^{12}-71 q^{11}+9 q^{10}+117 q^9+15 q^8-157 q^7-67 q^6+198 q^5+129 q^4-216 q^3-214 q^2+230 q+287-207 q^{-1} -375 q^{-2} +187 q^{-3} +436 q^{-4} -137 q^{-5} -500 q^{-6} +93 q^{-7} +535 q^{-8} -36 q^{-9} -553 q^{-10} -19 q^{-11} +546 q^{-12} +67 q^{-13} -510 q^{-14} -105 q^{-15} +452 q^{-16} +124 q^{-17} -373 q^{-18} -130 q^{-19} +293 q^{-20} +114 q^{-21} -213 q^{-22} -91 q^{-23} +146 q^{-24} +66 q^{-25} -97 q^{-26} -40 q^{-27} +59 q^{-28} +24 q^{-29} -36 q^{-30} -12 q^{-31} +20 q^{-32} +6 q^{-33} -11 q^{-34} - q^{-35} +3 q^{-36} +2 q^{-37} -3 q^{-38} + q^{-39} </math> | |
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{{Computer Talk Header}} |
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coloured_jones_4 = <math>q^{36}-3 q^{35}+5 q^{33}+6 q^{31}-20 q^{30}-10 q^{29}+20 q^{28}+15 q^{27}+48 q^{26}-64 q^{25}-73 q^{24}+8 q^{23}+45 q^{22}+206 q^{21}-67 q^{20}-196 q^{19}-141 q^{18}-28 q^{17}+507 q^{16}+119 q^{15}-231 q^{14}-445 q^{13}-398 q^{12}+757 q^{11}+517 q^{10}+69 q^9-692 q^8-1095 q^7+682 q^6+898 q^5+746 q^4-604 q^3-1864 q^2+210 q+981+1579 q^{-1} -122 q^{-2} -2422 q^{-3} -475 q^{-4} +713 q^{-5} +2302 q^{-6} +577 q^{-7} -2665 q^{-8} -1157 q^{-9} +235 q^{-10} +2791 q^{-11} +1288 q^{-12} -2619 q^{-13} -1710 q^{-14} -320 q^{-15} +2980 q^{-16} +1883 q^{-17} -2279 q^{-18} -2026 q^{-19} -874 q^{-20} +2774 q^{-21} +2217 q^{-22} -1656 q^{-23} -1940 q^{-24} -1285 q^{-25} +2135 q^{-26} +2127 q^{-27} -916 q^{-28} -1432 q^{-29} -1359 q^{-30} +1293 q^{-31} +1608 q^{-32} -361 q^{-33} -749 q^{-34} -1057 q^{-35} +600 q^{-36} +929 q^{-37} -119 q^{-38} -235 q^{-39} -609 q^{-40} +230 q^{-41} +409 q^{-42} -74 q^{-43} -12 q^{-44} -266 q^{-45} +91 q^{-46} +144 q^{-47} -63 q^{-48} +27 q^{-49} -92 q^{-50} +41 q^{-51} +44 q^{-52} -37 q^{-53} +16 q^{-54} -26 q^{-55} +14 q^{-56} +12 q^{-57} -13 q^{-58} +5 q^{-59} -5 q^{-60} +3 q^{-61} +2 q^{-62} -3 q^{-63} + q^{-64} </math> | |
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coloured_jones_5 = <math>q^{55}-3 q^{54}+5 q^{52}-q^{49}-13 q^{48}-10 q^{47}+20 q^{46}+24 q^{45}+15 q^{44}-3 q^{43}-57 q^{42}-73 q^{41}-3 q^{40}+98 q^{39}+136 q^{38}+81 q^{37}-98 q^{36}-274 q^{35}-231 q^{34}+48 q^{33}+388 q^{32}+488 q^{31}+156 q^{30}-440 q^{29}-822 q^{28}-557 q^{27}+309 q^{26}+1162 q^{25}+1143 q^{24}+98 q^{23}-1294 q^{22}-1893 q^{21}-890 q^{20}+1169 q^{19}+2580 q^{18}+1963 q^{17}-495 q^{16}-3034 q^{15}-3320 q^{14}-616 q^{13}+3036 q^{12}+4575 q^{11}+2290 q^{10}-2444 q^9-5669 q^8-4183 q^7+1215 q^6+6215 q^5+6272 q^4+563 q^3-6309 q^2-8086 q-2747+5675 q^{-1} +9762 q^{-2} +5110 q^{-3} -4708 q^{-4} -10866 q^{-5} -7467 q^{-6} +3196 q^{-7} +11732 q^{-8} +9709 q^{-9} -1663 q^{-10} -12094 q^{-11} -11696 q^{-12} -108 q^{-13} +12281 q^{-14} +13474 q^{-15} +1751 q^{-16} -12163 q^{-17} -14968 q^{-18} -3440 q^{-19} +11872 q^{-20} +16226 q^{-21} +5044 q^{-22} -11311 q^{-23} -17182 q^{-24} -6620 q^{-25} +10462 q^{-26} +17727 q^{-27} +8139 q^{-28} -9242 q^{-29} -17800 q^{-30} -9471 q^{-31} +7641 q^{-32} +17257 q^{-33} +10522 q^{-34} -5751 q^{-35} -16046 q^{-36} -11104 q^{-37} +3685 q^{-38} +14226 q^{-39} +11134 q^{-40} -1751 q^{-41} -11907 q^{-42} -10492 q^{-43} +49 q^{-44} +9366 q^{-45} +9335 q^{-46} +1143 q^{-47} -6881 q^{-48} -7734 q^{-49} -1824 q^{-50} +4654 q^{-51} +6007 q^{-52} +2020 q^{-53} -2896 q^{-54} -4354 q^{-55} -1827 q^{-56} +1630 q^{-57} +2906 q^{-58} +1475 q^{-59} -813 q^{-60} -1829 q^{-61} -1041 q^{-62} +366 q^{-63} +1045 q^{-64} +667 q^{-65} -136 q^{-66} -563 q^{-67} -378 q^{-68} +44 q^{-69} +279 q^{-70} +195 q^{-71} -23 q^{-72} -131 q^{-73} -73 q^{-74} +8 q^{-75} +49 q^{-76} +40 q^{-77} -15 q^{-78} -33 q^{-79} +5 q^{-80} +11 q^{-81} -4 q^{-82} +11 q^{-83} -5 q^{-84} -15 q^{-85} +10 q^{-86} +6 q^{-87} -7 q^{-88} +3 q^{-89} + q^{-90} -5 q^{-91} +3 q^{-92} +2 q^{-93} -3 q^{-94} + q^{-95} </math> | |
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<table> |
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coloured_jones_6 = <math>q^{78}-3 q^{77}+5 q^{75}-7 q^{72}+6 q^{71}-13 q^{70}-10 q^{69}+29 q^{68}+15 q^{67}+15 q^{66}-27 q^{65}+4 q^{64}-68 q^{63}-73 q^{62}+62 q^{61}+89 q^{60}+135 q^{59}+9 q^{58}+63 q^{57}-242 q^{56}-367 q^{55}-95 q^{54}+110 q^{53}+456 q^{52}+367 q^{51}+601 q^{50}-255 q^{49}-953 q^{48}-932 q^{47}-608 q^{46}+398 q^{45}+974 q^{44}+2312 q^{43}+1026 q^{42}-733 q^{41}-2167 q^{40}-2865 q^{39}-1764 q^{38}-12 q^{37}+4402 q^{36}+4486 q^{35}+2707 q^{34}-1036 q^{33}-5025 q^{32}-6815 q^{31}-5672 q^{30}+2853 q^{29}+7427 q^{28}+9801 q^{27}+6133 q^{26}-1711 q^{25}-10728 q^{24}-15749 q^{23}-6530 q^{22}+3169 q^{21}+14993 q^{20}+18223 q^{19}+11488 q^{18}-5657 q^{17}-23111 q^{16}-21653 q^{15}-12620 q^{14}+9494 q^{13}+26828 q^{12}+31357 q^{11}+12391 q^{10}-18421 q^9-33135 q^8-35689 q^7-10156 q^6+22642 q^5+47836 q^4+38313 q^3+1043 q^2-32044 q-55786-38220 q^{-1} +3894 q^{-2} +52563 q^{-3} +62043 q^{-4} +29106 q^{-5} -17439 q^{-6} -65382 q^{-7} -65037 q^{-8} -22978 q^{-9} +45146 q^{-10} +76917 q^{-11} +56713 q^{-12} +4383 q^{-13} -64503 q^{-14} -84666 q^{-15} -49669 q^{-16} +31243 q^{-17} +83078 q^{-18} +78682 q^{-19} +26256 q^{-20} -57964 q^{-21} -97096 q^{-22} -71826 q^{-23} +16414 q^{-24} +84162 q^{-25} +94960 q^{-26} +45142 q^{-27} -49560 q^{-28} -104730 q^{-29} -89622 q^{-30} +1943 q^{-31} +82006 q^{-32} +107014 q^{-33} +62045 q^{-34} -38712 q^{-35} -107583 q^{-36} -104025 q^{-37} -14318 q^{-38} +74179 q^{-39} +113419 q^{-40} +77868 q^{-41} -22271 q^{-42} -101680 q^{-43} -112526 q^{-44} -33077 q^{-45} +56857 q^{-46} +109001 q^{-47} +89073 q^{-48} -124 q^{-49} -82953 q^{-50} -109059 q^{-51} -49394 q^{-52} +30992 q^{-53} +89805 q^{-54} +88627 q^{-55} +21109 q^{-56} -53732 q^{-57} -90038 q^{-58} -55055 q^{-59} +4988 q^{-60} +59611 q^{-61} +73183 q^{-62} +32174 q^{-63} -24051 q^{-64} -60527 q^{-65} -46714 q^{-66} -11158 q^{-67} +29527 q^{-68} +48458 q^{-69} +29880 q^{-70} -4180 q^{-71} -31958 q^{-72} -30078 q^{-73} -14530 q^{-74} +9323 q^{-75} +25188 q^{-76} +19731 q^{-77} +3455 q^{-78} -12899 q^{-79} -14492 q^{-80} -10274 q^{-81} +543 q^{-82} +10205 q^{-83} +9688 q^{-84} +3611 q^{-85} -3947 q^{-86} -5031 q^{-87} -5025 q^{-88} -1321 q^{-89} +3269 q^{-90} +3610 q^{-91} +1822 q^{-92} -997 q^{-93} -1077 q^{-94} -1814 q^{-95} -920 q^{-96} +891 q^{-97} +1025 q^{-98} +595 q^{-99} -302 q^{-100} +10 q^{-101} -487 q^{-102} -392 q^{-103} +249 q^{-104} +219 q^{-105} +123 q^{-106} -142 q^{-107} +128 q^{-108} -92 q^{-109} -132 q^{-110} +83 q^{-111} +36 q^{-112} +12 q^{-113} -70 q^{-114} +67 q^{-115} -10 q^{-116} -40 q^{-117} +29 q^{-118} +3 q^{-119} +2 q^{-120} -26 q^{-121} +21 q^{-122} +2 q^{-123} -13 q^{-124} +9 q^{-125} - q^{-126} + q^{-127} -5 q^{-128} +3 q^{-129} +2 q^{-130} -3 q^{-131} + q^{-132} </math> | |
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coloured_jones_7 = <math>q^{105}-3 q^{104}+5 q^{102}-7 q^{99}+6 q^{97}-13 q^{96}-q^{95}+20 q^{94}+15 q^{93}+15 q^{92}-27 q^{91}-31 q^{90}+4 q^{89}-57 q^{88}-19 q^{87}+53 q^{86}+89 q^{85}+148 q^{84}+8 q^{83}-88 q^{82}-83 q^{81}-269 q^{80}-229 q^{79}-34 q^{78}+170 q^{77}+605 q^{76}+500 q^{75}+218 q^{74}+6 q^{73}-756 q^{72}-1064 q^{71}-1000 q^{70}-557 q^{69}+908 q^{68}+1732 q^{67}+1973 q^{66}+1827 q^{65}-112 q^{64}-1965 q^{63}-3479 q^{62}-4216 q^{61}-1785 q^{60}+1249 q^{59}+4471 q^{58}+7157 q^{57}+5569 q^{56}+1829 q^{55}-3848 q^{54}-10138 q^{53}-10979 q^{52}-7761 q^{51}-50 q^{50}+10960 q^{49}+16620 q^{48}+16829 q^{47}+8893 q^{46}-7103 q^{45}-20157 q^{44}-27579 q^{43}-22959 q^{42}-3654 q^{41}+17772 q^{40}+36288 q^{39}+40873 q^{38}+23044 q^{37}-5655 q^{36}-38811 q^{35}-58918 q^{34}-49299 q^{33}-18218 q^{32}+29217 q^{31}+70628 q^{30}+79120 q^{29}+54279 q^{28}-4146 q^{27}-70199 q^{26}-105251 q^{25}-98015 q^{24}-37985 q^{23}+50949 q^{22}+120100 q^{21}+143664 q^{20}+94365 q^{19}-10861 q^{18}-116323 q^{17}-181668 q^{16}-158894 q^{15}-49939 q^{14}+89082 q^{13}+204314 q^{12}+223127 q^{11}+125841 q^{10}-37376 q^9-204535 q^8-278016 q^7-209941 q^6-35602 q^5+180193 q^4+315818 q^3+292537 q^2+123886 q-131266-332406 q^{-1} -366700 q^{-2} -219039 q^{-3} +63541 q^{-4} +326287 q^{-5} +425090 q^{-6} +313588 q^{-7} +18020 q^{-8} -300224 q^{-9} -466762 q^{-10} -400552 q^{-11} -104271 q^{-12} +258719 q^{-13} +489935 q^{-14} +475838 q^{-15} +190604 q^{-16} -207640 q^{-17} -499106 q^{-18} -537948 q^{-19} -270228 q^{-20} +153051 q^{-21} +496546 q^{-22} +586987 q^{-23} +341870 q^{-24} -99047 q^{-25} -487955 q^{-26} -625688 q^{-27} -403628 q^{-28} +49238 q^{-29} +476008 q^{-30} +656253 q^{-31} +457319 q^{-32} -3979 q^{-33} -463670 q^{-34} -681906 q^{-35} -504643 q^{-36} -37239 q^{-37} +451185 q^{-38} +704227 q^{-39} +548224 q^{-40} +76868 q^{-41} -437224 q^{-42} -723423 q^{-43} -590117 q^{-44} -118240 q^{-45} +418986 q^{-46} +738229 q^{-47} +630766 q^{-48} +163718 q^{-49} -392270 q^{-50} -744700 q^{-51} -669088 q^{-52} -215267 q^{-53} +353345 q^{-54} +738647 q^{-55} +701339 q^{-56} +271792 q^{-57} -299629 q^{-58} -714860 q^{-59} -722203 q^{-60} -329990 q^{-61} +231138 q^{-62} +669613 q^{-63} +725758 q^{-64} +384010 q^{-65} -151130 q^{-66} -602189 q^{-67} -706850 q^{-68} -426152 q^{-69} +66032 q^{-70} +514775 q^{-71} +662652 q^{-72} +450056 q^{-73} +15962 q^{-74} -414116 q^{-75} -594816 q^{-76} -450571 q^{-77} -85577 q^{-78} +308775 q^{-79} +507937 q^{-80} +426833 q^{-81} +136688 q^{-82} -208698 q^{-83} -411023 q^{-84} -382051 q^{-85} -165017 q^{-86} +122682 q^{-87} +313046 q^{-88} +322316 q^{-89} +171536 q^{-90} -55721 q^{-91} -223315 q^{-92} -256327 q^{-93} -160059 q^{-94} +10073 q^{-95} +148231 q^{-96} +191585 q^{-97} +136538 q^{-98} +16367 q^{-99} -90360 q^{-100} -134545 q^{-101} -108038 q^{-102} -27646 q^{-103} +50119 q^{-104} +88736 q^{-105} +79332 q^{-106} +28709 q^{-107} -24306 q^{-108} -54708 q^{-109} -54676 q^{-110} -24540 q^{-111} +9734 q^{-112} +31648 q^{-113} +35373 q^{-114} +18291 q^{-115} -2489 q^{-116} -17000 q^{-117} -21548 q^{-118} -12382 q^{-119} -548 q^{-120} +8471 q^{-121} +12522 q^{-122} +7721 q^{-123} +1268 q^{-124} -3923 q^{-125} -6875 q^{-126} -4360 q^{-127} -1171 q^{-128} +1531 q^{-129} +3622 q^{-130} +2379 q^{-131} +852 q^{-132} -574 q^{-133} -1911 q^{-134} -1089 q^{-135} -426 q^{-136} +73 q^{-137} +862 q^{-138} +505 q^{-139} +325 q^{-140} +31 q^{-141} -530 q^{-142} -169 q^{-143} -48 q^{-144} -66 q^{-145} +162 q^{-146} +27 q^{-147} +107 q^{-148} +71 q^{-149} -168 q^{-150} -3 q^{-151} +32 q^{-152} -28 q^{-153} +24 q^{-154} -36 q^{-155} +34 q^{-156} +38 q^{-157} -58 q^{-158} +8 q^{-159} +18 q^{-160} -5 q^{-161} +4 q^{-162} -19 q^{-163} +10 q^{-164} +13 q^{-165} -17 q^{-166} +3 q^{-167} +5 q^{-168} - q^{-169} + q^{-170} -5 q^{-171} +3 q^{-172} +2 q^{-173} -3 q^{-174} + q^{-175} </math> | |
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:= </pre></td> |
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computer_talk = |
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<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
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<table> |
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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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<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>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 41]]</nowiki></pre></td></tr> |
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<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
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<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[1, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], |
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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, 41]]</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, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], |
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X[9, 20, 10, 1], X[15, 19, 16, 18], X[13, 8, 14, 9], X[17, 6, 18, 7], |
X[9, 20, 10, 1], X[15, 19, 16, 18], X[13, 8, 14, 9], X[17, 6, 18, 7], |
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X[7, 16, 8, 17], X[19, 15, 20, 14]]</nowiki></ |
X[7, 16, 8, 17], X[19, 15, 20, 14]]</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, 41]]</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, 4, -3, 1, -2, 8, -9, 7, -5, 3, -4, 2, -7, 10, -6, 9, -8, |
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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, 41]]</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, 4, -3, 1, -2, 8, -9, 7, -5, 3, -4, 2, -7, 10, -6, 9, -8, |
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6, -10, 5]</nowiki></ |
6, -10, 5]</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, 41]]</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[5, {1, -2, 1, -2, -2, 3, -2, -4, 3, -4}]</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, 41]]</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[4, 10, 12, 16, 20, 2, 8, 18, 6, 14]</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, 41]]</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[5, {1, -2, 1, -2, -2, 3, -2, -4, 3, -4}]</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>{5, 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, 41]]</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>5</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, 41]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:10_41_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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<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, 41]]&) /@ { |
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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, 2, 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, 41]][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> -3 7 17 2 3 |
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-21 + t - -- + -- + 17 t - 7 t + t |
-21 + t - -- + -- + 17 t - 7 t + t |
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2 t |
2 t |
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t</nowiki></ |
t</nowiki></code></td></tr> |
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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, 41]][z]</nowiki></pre></td></tr> |
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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 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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1 - 2 z - 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, 41]][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, 41], Knot[11, NonAlternating, 5]}</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 |
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1 - 2 z - 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, 41]][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> -7 3 6 9 11 12 11 2 3 |
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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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<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, 41], Knot[11, NonAlternating, 5]}</nowiki></code></td></tr> |
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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, 41]], KnotSignature[Knot[10, 41]]}</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>{71, -2}</nowiki></code></td></tr> |
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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, 41]][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> -7 3 6 9 11 12 11 2 3 |
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-8 + q - -- + -- - -- + -- - -- + -- + 6 q - 3 q + q |
-8 + q - -- + -- - -- + -- - -- + -- + 6 q - 3 q + q |
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6 5 4 3 2 q |
6 5 4 3 2 q |
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q q q q q</nowiki></ |
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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<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, 41], Knot[10, 94]}</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 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> -22 -18 2 2 -10 2 2 2 2 2 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, 41], Knot[10, 94]}</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[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, 41]][q]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -22 -18 2 2 -10 2 2 2 2 2 4 |
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1 + q - q + --- - --- + q - -- + -- - -- + -- - q + 2 q - |
1 + q - q + --- - --- + q - -- + -- - -- + -- - q + 2 q - |
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16 14 8 6 4 2 |
16 14 8 6 4 2 |
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| Line 99: | Line 181: | ||
6 10 |
6 10 |
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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, 41]][a, z]</nowiki></pre></td></tr> |
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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 |
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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, 41]][a, z]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 |
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-2 2 4 6 2 z 2 2 4 2 6 2 |
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-1 + a + 2 a - 2 a + a - 4 z + -- + 4 a z - 4 a z + a z - |
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2 |
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a |
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4 2 4 4 4 2 6 |
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2 z + 3 a z - 2 a z + a z</nowiki></code></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[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, 41]][a, z]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 |
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-2 2 4 6 z 3 7 2 3 z |
-2 2 4 6 z 3 7 2 3 z |
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-1 - a - 2 a - 2 a - a - - - 2 a z - 2 a z + a z + 7 z + ---- + |
-1 - a - 2 a - 2 a - a - - - 2 a z - 2 a z + a z + 7 z + ---- + |
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| Line 130: | Line 231: | ||
8 2 8 4 8 9 3 9 |
8 2 8 4 8 9 3 9 |
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3 z + 6 a z + 3 a z + a z + a z</nowiki></ |
3 z + 6 a z + 3 a z + a z + 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, 41]], Vassiliev[3][Knot[10, 41]]}</nowiki></pre></td></tr> |
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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, 2}</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, 41]], Vassiliev[3][Knot[10, 41]]}</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{-2, 2}</nowiki></code></td></tr> |
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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, 41]][q, t]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>5 7 1 2 1 4 2 5 4 |
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-- + - + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
-- + - + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
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3 q 15 6 13 5 11 5 11 4 9 4 9 3 7 3 |
3 q 15 6 13 5 11 5 11 4 9 4 9 3 7 3 |
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| Line 145: | Line 256: | ||
3 3 5 3 7 4 |
3 3 5 3 7 4 |
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q t + 2 q t + q t</nowiki></ |
q t + 2 q t + q t</nowiki></code></td></tr> |
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</table> |
</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 41], 2][q]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -20 3 2 7 17 8 24 47 18 53 |
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-19 + q - --- + --- + --- - --- + --- + --- - --- + --- + --- - |
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19 18 17 16 15 14 13 12 11 |
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q q q q q q q q q |
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86 22 85 110 12 103 104 6 97 74 2 |
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--- + -- + -- - --- + -- + --- - --- - -- + -- - -- + 71 q - 37 q - |
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10 9 8 7 6 5 4 3 2 q |
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q q q q q q q q q |
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3 4 5 6 7 9 10 |
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22 q + 37 q - 10 q - 13 q + 11 q - 3 q + q</nowiki></code></td></tr> |
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</table> }} |
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Latest revision as of 17:02, 1 September 2005
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 41's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
| Planar diagram presentation | X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X9,20,10,1 X15,19,16,18 X13,8,14,9 X17,6,18,7 X7,16,8,17 X19,15,20,14 |
| Gauss code | -1, 4, -3, 1, -2, 8, -9, 7, -5, 3, -4, 2, -7, 10, -6, 9, -8, 6, -10, 5 |
| Dowker-Thistlethwaite code | 4 10 12 16 20 2 8 18 6 14 |
| Conway Notation | [221212] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 |
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 [{12, 7}, {1, 10}, {11, 8}, {7, 9}, {10, 12}, {6, 11}, {8, 2}, {3, 1}, {2, 5}, {4, 6}, {5, 3}, {9, 4}] |
[edit Notes on presentations of 10 41]
Computer Talk
The above data is available with the Mathematica package
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 41"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X9,20,10,1 X15,19,16,18 X13,8,14,9 X17,6,18,7 X7,16,8,17 X19,15,20,14 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 4, -3, 1, -2, 8, -9, 7, -5, 3, -4, 2, -7, 10, -6, 9, -8, 6, -10, 5 |
In[6]:=
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DTCode[K]
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Out[6]=
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4 10 12 16 20 2 8 18 6 14 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
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ConwayNotation[K]
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Out[8]=
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[221212] |
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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{BR}(5,\{1,-2,1,-2,-2,3,-2,-4,3,-4\})} |
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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{ 5, 10, 5 } |
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[{12, 7}, {1, 10}, {11, 8}, {7, 9}, {10, 12}, {6, 11}, {8, 2}, {3, 1}, {2, 5}, {4, 6}, {5, 3}, {9, 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
| Alexander polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^3-7 t^2+17 t-21+17 t^{-1} -7 t^{-2} + t^{-3} } |
| Conway polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^6-z^4-2 z^2+1} |
| 2nd Alexander ideal (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}} |
| Determinant and Signature | { 71, -2 } |
| Jones polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^3-3 q^2+6 q-8+11 q^{-1} -12 q^{-2} +11 q^{-3} -9 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} } |
| HOMFLY-PT polynomial (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^2 a^6+a^6-2 z^4 a^4-4 z^2 a^4-2 a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+2 a^2-2 z^4-4 z^2-1+z^2 a^{-2} + a^{-2} } |
| Kauffman polynomial (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^3 z^9+a z^9+3 a^4 z^8+6 a^2 z^8+3 z^8+5 a^5 z^7+8 a^3 z^7+6 a z^7+3 z^7 a^{-1} +5 a^6 z^6+4 a^4 z^6-7 a^2 z^6+z^6 a^{-2} -5 z^6+3 a^7 z^5-4 a^5 z^5-18 a^3 z^5-20 a z^5-9 z^5 a^{-1} +a^8 z^4-6 a^6 z^4-14 a^4 z^4-8 a^2 z^4-3 z^4 a^{-2} -4 z^4-3 a^7 z^3+a^5 z^3+10 a^3 z^3+13 a z^3+7 z^3 a^{-1} -a^8 z^2+4 a^6 z^2+10 a^4 z^2+9 a^2 z^2+3 z^2 a^{-2} +7 z^2+a^7 z-2 a^3 z-2 a z-z a^{-1} -a^6-2 a^4-2 a^2- a^{-2} -1} |
| The A2 invariant | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{22}-q^{18}+2 q^{16}-2 q^{14}+q^{10}-2 q^8+2 q^6-2 q^4+2 q^2+1- q^{-2} +2 q^{-4} - q^{-6} + q^{-10} } |
| The G2 invariant | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{114}-2 q^{112}+4 q^{110}-6 q^{108}+5 q^{106}-4 q^{104}-2 q^{102}+12 q^{100}-21 q^{98}+30 q^{96}-32 q^{94}+22 q^{92}-3 q^{90}-23 q^{88}+55 q^{86}-74 q^{84}+80 q^{82}-61 q^{80}+20 q^{78}+31 q^{76}-80 q^{74}+112 q^{72}-114 q^{70}+80 q^{68}-22 q^{66}-44 q^{64}+90 q^{62}-97 q^{60}+69 q^{58}-13 q^{56}-47 q^{54}+74 q^{52}-64 q^{50}+9 q^{48}+67 q^{46}-125 q^{44}+139 q^{42}-91 q^{40}+101 q^{36}-178 q^{34}+196 q^{32}-153 q^{30}+59 q^{28}+49 q^{26}-132 q^{24}+169 q^{22}-140 q^{20}+70 q^{18}+11 q^{16}-77 q^{14}+96 q^{12}-70 q^{10}+13 q^8+57 q^6-97 q^4+94 q^2-42-35 q^{-2} +106 q^{-4} -142 q^{-6} +126 q^{-8} -69 q^{-10} -11 q^{-12} +83 q^{-14} -120 q^{-16} +119 q^{-18} -77 q^{-20} +22 q^{-22} +24 q^{-24} -54 q^{-26} +57 q^{-28} -43 q^{-30} +24 q^{-32} -2 q^{-34} -9 q^{-36} +12 q^{-38} -10 q^{-40} +6 q^{-42} -2 q^{-44} + q^{-46} } |
Further Quantum Invariants
Further quantum knot invariants for 10_41.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{15}-2 q^{13}+3 q^{11}-3 q^9+2 q^7-q^5-q^3+3 q-2 q^{-1} +3 q^{-3} -2 q^{-5} + q^{-7} } |
| 2 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{42}-2 q^{40}+6 q^{36}-8 q^{34}-2 q^{32}+15 q^{30}-15 q^{28}-5 q^{26}+24 q^{24}-15 q^{22}-11 q^{20}+21 q^{18}-3 q^{16}-13 q^{14}+5 q^{12}+11 q^{10}-7 q^8-13 q^6+17 q^4+4 q^2-22+15 q^{-2} +12 q^{-4} -22 q^{-6} +5 q^{-8} +14 q^{-10} -12 q^{-12} -2 q^{-14} +8 q^{-16} -2 q^{-18} -2 q^{-20} + q^{-22} } |
| 3 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{81}-2 q^{79}+3 q^{75}+q^{73}-7 q^{71}-3 q^{69}+14 q^{67}+3 q^{65}-22 q^{63}-4 q^{61}+35 q^{59}+7 q^{57}-54 q^{55}-12 q^{53}+75 q^{51}+24 q^{49}-92 q^{47}-44 q^{45}+103 q^{43}+64 q^{41}-96 q^{39}-86 q^{37}+73 q^{35}+98 q^{33}-39 q^{31}-96 q^{29}-2 q^{27}+84 q^{25}+41 q^{23}-62 q^{21}-73 q^{19}+39 q^{17}+92 q^{15}-9 q^{13}-108 q^{11}-14 q^9+111 q^7+41 q^5-108 q^3-65 q+96 q^{-1} +87 q^{-3} -71 q^{-5} -103 q^{-7} +44 q^{-9} +103 q^{-11} -11 q^{-13} -92 q^{-15} -16 q^{-17} +70 q^{-19} +33 q^{-21} -45 q^{-23} -34 q^{-25} +20 q^{-27} +29 q^{-29} -4 q^{-31} -19 q^{-33} -2 q^{-35} +8 q^{-37} +3 q^{-39} -2 q^{-41} -2 q^{-43} + q^{-45} } |
| 4 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{132}-2 q^{130}+3 q^{126}-2 q^{124}+2 q^{122}-8 q^{120}+2 q^{118}+13 q^{116}-8 q^{114}+3 q^{112}-21 q^{110}+11 q^{108}+38 q^{106}-28 q^{104}-17 q^{102}-43 q^{100}+57 q^{98}+107 q^{96}-67 q^{94}-106 q^{92}-117 q^{90}+148 q^{88}+287 q^{86}-56 q^{84}-279 q^{82}-324 q^{80}+196 q^{78}+566 q^{76}+118 q^{74}-396 q^{72}-638 q^{70}+41 q^{68}+734 q^{66}+432 q^{64}-251 q^{62}-806 q^{60}-287 q^{58}+555 q^{56}+629 q^{54}+121 q^{52}-619 q^{50}-529 q^{48}+110 q^{46}+521 q^{44}+435 q^{42}-188 q^{40}-522 q^{38}-316 q^{36}+238 q^{34}+554 q^{32}+214 q^{30}-381 q^{28}-570 q^{26}-15 q^{24}+538 q^{22}+492 q^{20}-219 q^{18}-708 q^{16}-230 q^{14}+452 q^{12}+695 q^{10}-4 q^8-727 q^6-459 q^4+226 q^2+784+302 q^{-2} -531 q^{-4} -614 q^{-6} -142 q^{-8} +627 q^{-10} +539 q^{-12} -138 q^{-14} -519 q^{-16} -444 q^{-18} +253 q^{-20} +500 q^{-22} +200 q^{-24} -198 q^{-26} -448 q^{-28} -78 q^{-30} +226 q^{-32} +261 q^{-34} +75 q^{-36} -226 q^{-38} -153 q^{-40} -4 q^{-42} +119 q^{-44} +122 q^{-46} -36 q^{-48} -66 q^{-50} -54 q^{-52} +9 q^{-54} +53 q^{-56} +11 q^{-58} -4 q^{-60} -19 q^{-62} -9 q^{-64} +8 q^{-66} +3 q^{-68} +3 q^{-70} -2 q^{-72} -2 q^{-74} + q^{-76} } |
| 5 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{195}-2 q^{193}+3 q^{189}-2 q^{187}-q^{185}+q^{183}-3 q^{181}+q^{179}+8 q^{177}-2 q^{175}-8 q^{173}+3 q^{169}+8 q^{167}+3 q^{165}-15 q^{163}-25 q^{161}+4 q^{159}+57 q^{157}+54 q^{155}-24 q^{153}-122 q^{151}-130 q^{149}+25 q^{147}+255 q^{145}+291 q^{143}-14 q^{141}-446 q^{139}-559 q^{137}-87 q^{135}+679 q^{133}+1001 q^{131}+338 q^{129}-928 q^{127}-1605 q^{125}-797 q^{123}+1064 q^{121}+2328 q^{119}+1542 q^{117}-983 q^{115}-3066 q^{113}-2521 q^{111}+580 q^{109}+3604 q^{107}+3607 q^{105}+227 q^{103}-3758 q^{101}-4635 q^{99}-1307 q^{97}+3405 q^{95}+5278 q^{93}+2520 q^{91}-2506 q^{89}-5400 q^{87}-3601 q^{85}+1259 q^{83}+4895 q^{81}+4283 q^{79}+144 q^{77}-3856 q^{75}-4468 q^{73}-1437 q^{71}+2519 q^{69}+4152 q^{67}+2398 q^{65}-1093 q^{63}-3476 q^{61}-3006 q^{59}-185 q^{57}+2666 q^{55}+3284 q^{53}+1215 q^{51}-1880 q^{49}-3381 q^{47}-1971 q^{45}+1209 q^{43}+3423 q^{41}+2571 q^{39}-722 q^{37}-3474 q^{35}-3065 q^{33}+267 q^{31}+3539 q^{29}+3608 q^{27}+194 q^{25}-3571 q^{23}-4120 q^{21}-816 q^{19}+3413 q^{17}+4641 q^{15}+1596 q^{13}-3003 q^{11}-4973 q^9-2494 q^7+2226 q^5+5006 q^3+3405 q-1142 q^{-1} -4632 q^{-3} -4092 q^{-5} -130 q^{-7} +3773 q^{-9} +4413 q^{-11} +1406 q^{-13} -2576 q^{-15} -4216 q^{-17} -2395 q^{-19} +1172 q^{-21} +3521 q^{-23} +2931 q^{-25} +146 q^{-27} -2466 q^{-29} -2922 q^{-31} -1137 q^{-33} +1293 q^{-35} +2434 q^{-37} +1635 q^{-39} -230 q^{-41} -1667 q^{-43} -1674 q^{-45} -475 q^{-47} +861 q^{-49} +1333 q^{-51} +795 q^{-53} -192 q^{-55} -866 q^{-57} -787 q^{-59} -182 q^{-61} +409 q^{-63} +575 q^{-65} +321 q^{-67} -86 q^{-69} -338 q^{-71} -288 q^{-73} -60 q^{-75} +141 q^{-77} +182 q^{-79} +98 q^{-81} -23 q^{-83} -97 q^{-85} -74 q^{-87} -11 q^{-89} +33 q^{-91} +35 q^{-93} +20 q^{-95} -4 q^{-97} -19 q^{-99} -9 q^{-101} + q^{-103} +3 q^{-105} +3 q^{-107} +3 q^{-109} -2 q^{-111} -2 q^{-113} + q^{-115} } |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{22}-q^{18}+2 q^{16}-2 q^{14}+q^{10}-2 q^8+2 q^6-2 q^4+2 q^2+1- q^{-2} +2 q^{-4} - q^{-6} + q^{-10} } |
| 1,1 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{60}-4 q^{58}+10 q^{56}-20 q^{54}+40 q^{52}-70 q^{50}+110 q^{48}-162 q^{46}+227 q^{44}-302 q^{42}+372 q^{40}-436 q^{38}+485 q^{36}-506 q^{34}+478 q^{32}-394 q^{30}+262 q^{28}-66 q^{26}-170 q^{24}+432 q^{22}-689 q^{20}+904 q^{18}-1060 q^{16}+1128 q^{14}-1105 q^{12}+994 q^{10}-798 q^8+548 q^6-275 q^4+6 q^2+240-432 q^{-2} +554 q^{-4} -602 q^{-6} +588 q^{-8} -524 q^{-10} +427 q^{-12} -316 q^{-14} +218 q^{-16} -134 q^{-18} +74 q^{-20} -36 q^{-22} +14 q^{-24} -4 q^{-26} + q^{-28} } |
| 2,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{56}-q^{52}+2 q^{48}-5 q^{44}+q^{42}+6 q^{40}-5 q^{38}-8 q^{36}+6 q^{34}+11 q^{32}-7 q^{30}-9 q^{28}+11 q^{26}+8 q^{24}-10 q^{22}-3 q^{20}+8 q^{18}-4 q^{16}-4 q^{14}+4 q^{12}+q^{10}-7 q^8+3 q^6+10 q^4-7 q^2-6+10 q^{-2} +6 q^{-4} -11 q^{-6} -4 q^{-8} +8 q^{-10} +4 q^{-12} -6 q^{-14} -3 q^{-16} +6 q^{-18} +3 q^{-20} -2 q^{-22} -2 q^{-24} + q^{-28} } |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{48}-2 q^{46}+5 q^{42}-7 q^{40}-2 q^{38}+14 q^{36}-10 q^{34}-7 q^{32}+20 q^{30}-9 q^{28}-12 q^{26}+18 q^{24}-4 q^{22}-11 q^{20}+8 q^{18}+3 q^{16}-4 q^{14}-7 q^{12}+9 q^{10}+5 q^8-17 q^6+9 q^4+12 q^2-17+5 q^{-2} +12 q^{-4} -14 q^{-6} +4 q^{-8} +7 q^{-10} -7 q^{-12} +3 q^{-14} +2 q^{-16} -2 q^{-18} + q^{-20} } |
| 1,0,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{29}+q^{25}-q^{23}+2 q^{21}-3 q^{19}+q^{17}-2 q^{15}+q^{13}-q^{11}+q^9+q^7-q^5+2 q^3-q+2 q^{-1} -2 q^{-3} +2 q^{-5} - q^{-7} + q^{-9} + q^{-13} } |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{48}-2 q^{46}+4 q^{44}-7 q^{42}+11 q^{40}-14 q^{38}+18 q^{36}-20 q^{34}+21 q^{32}-20 q^{30}+15 q^{28}-8 q^{26}-2 q^{24}+12 q^{22}-23 q^{20}+32 q^{18}-39 q^{16}+42 q^{14}-41 q^{12}+37 q^{10}-29 q^8+19 q^6-7 q^4-2 q^2+11-17 q^{-2} +22 q^{-4} -22 q^{-6} +20 q^{-8} -17 q^{-10} +13 q^{-12} -9 q^{-14} +6 q^{-16} -2 q^{-18} + q^{-20} } |
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{78}-2 q^{74}-2 q^{72}+2 q^{70}+6 q^{68}+q^{66}-9 q^{64}-8 q^{62}+6 q^{60}+16 q^{58}+3 q^{56}-17 q^{54}-14 q^{52}+10 q^{50}+22 q^{48}+q^{46}-21 q^{44}-11 q^{42}+15 q^{40}+17 q^{38}-8 q^{36}-18 q^{34}+2 q^{32}+17 q^{30}+3 q^{28}-15 q^{26}-6 q^{24}+12 q^{22}+8 q^{20}-11 q^{18}-10 q^{16}+10 q^{14}+13 q^{12}-8 q^{10}-19 q^8+2 q^6+22 q^4+10 q^2-18-19 q^{-2} +9 q^{-4} +24 q^{-6} +3 q^{-8} -19 q^{-10} -12 q^{-12} +11 q^{-14} +14 q^{-16} -2 q^{-18} -10 q^{-20} -3 q^{-22} +6 q^{-24} +4 q^{-26} -2 q^{-28} -2 q^{-30} + q^{-34} } |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{114}-2 q^{112}+4 q^{110}-6 q^{108}+5 q^{106}-4 q^{104}-2 q^{102}+12 q^{100}-21 q^{98}+30 q^{96}-32 q^{94}+22 q^{92}-3 q^{90}-23 q^{88}+55 q^{86}-74 q^{84}+80 q^{82}-61 q^{80}+20 q^{78}+31 q^{76}-80 q^{74}+112 q^{72}-114 q^{70}+80 q^{68}-22 q^{66}-44 q^{64}+90 q^{62}-97 q^{60}+69 q^{58}-13 q^{56}-47 q^{54}+74 q^{52}-64 q^{50}+9 q^{48}+67 q^{46}-125 q^{44}+139 q^{42}-91 q^{40}+101 q^{36}-178 q^{34}+196 q^{32}-153 q^{30}+59 q^{28}+49 q^{26}-132 q^{24}+169 q^{22}-140 q^{20}+70 q^{18}+11 q^{16}-77 q^{14}+96 q^{12}-70 q^{10}+13 q^8+57 q^6-97 q^4+94 q^2-42-35 q^{-2} +106 q^{-4} -142 q^{-6} +126 q^{-8} -69 q^{-10} -11 q^{-12} +83 q^{-14} -120 q^{-16} +119 q^{-18} -77 q^{-20} +22 q^{-22} +24 q^{-24} -54 q^{-26} +57 q^{-28} -43 q^{-30} +24 q^{-32} -2 q^{-34} -9 q^{-36} +12 q^{-38} -10 q^{-40} +6 q^{-42} -2 q^{-44} + q^{-46} } |
.
Computer Talk
The above data is available with the Mathematica package
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`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
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K = Knot["10 41"];
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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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^3-7 t^2+17 t-21+17 t^{-1} -7 t^{-2} + t^{-3} } |
In[5]:=
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Conway[K][z]
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Out[5]=
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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^6-z^4-2 z^2+1} |
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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}} |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 71, -2 } |
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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^3-3 q^2+6 q-8+11 q^{-1} -12 q^{-2} +11 q^{-3} -9 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} } |
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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^2 a^6+a^6-2 z^4 a^4-4 z^2 a^4-2 a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+2 a^2-2 z^4-4 z^2-1+z^2 a^{-2} + a^{-2} } |
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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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^3 z^9+a z^9+3 a^4 z^8+6 a^2 z^8+3 z^8+5 a^5 z^7+8 a^3 z^7+6 a z^7+3 z^7 a^{-1} +5 a^6 z^6+4 a^4 z^6-7 a^2 z^6+z^6 a^{-2} -5 z^6+3 a^7 z^5-4 a^5 z^5-18 a^3 z^5-20 a z^5-9 z^5 a^{-1} +a^8 z^4-6 a^6 z^4-14 a^4 z^4-8 a^2 z^4-3 z^4 a^{-2} -4 z^4-3 a^7 z^3+a^5 z^3+10 a^3 z^3+13 a z^3+7 z^3 a^{-1} -a^8 z^2+4 a^6 z^2+10 a^4 z^2+9 a^2 z^2+3 z^2 a^{-2} +7 z^2+a^7 z-2 a^3 z-2 a z-z a^{-1} -a^6-2 a^4-2 a^2- a^{-2} -1} |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11n5,}
Same Jones Polynomial (up to mirroring, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\leftrightarrow q^{-1}} ): {10_94,}
Computer Talk
The above data is available with the Mathematica package
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 41"];
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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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{ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^3-7 t^2+17 t-21+17 t^{-1} -7 t^{-2} + t^{-3} } , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^3-3 q^2+6 q-8+11 q^{-1} -12 q^{-2} +11 q^{-3} -9 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} } } |
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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{K11n5,} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{10_94,} |
Vassiliev invariants
| V2 and V3: | (-2, 2) |
| 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^rq^j} are shown, along with their alternating sums Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi} (fixed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , alternation over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} ). The squares with yellow highlighting are those on the "critical diagonals", where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s+1} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s-1} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=} -2 is the signature of 10 41. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
| Integral Khovanov Homology
(db, data source) |
|
The Coloured Jones Polynomials
The Coloured Jones Polynomials (in the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n+1}
-dimensional representation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sl(2)}
)
| Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n} |
| 2 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{10}-3 q^9+11 q^7-13 q^6-10 q^5+37 q^4-22 q^3-37 q^2+71 q-19-74 q^{-1} +97 q^{-2} -6 q^{-3} -104 q^{-4} +103 q^{-5} +12 q^{-6} -110 q^{-7} +85 q^{-8} +22 q^{-9} -86 q^{-10} +53 q^{-11} +18 q^{-12} -47 q^{-13} +24 q^{-14} +8 q^{-15} -17 q^{-16} +7 q^{-17} +2 q^{-18} -3 q^{-19} + q^{-20} } |
| 3 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{21}-3 q^{20}+5 q^{18}+6 q^{17}-13 q^{16}-17 q^{15}+20 q^{14}+39 q^{13}-22 q^{12}-71 q^{11}+9 q^{10}+117 q^9+15 q^8-157 q^7-67 q^6+198 q^5+129 q^4-216 q^3-214 q^2+230 q+287-207 q^{-1} -375 q^{-2} +187 q^{-3} +436 q^{-4} -137 q^{-5} -500 q^{-6} +93 q^{-7} +535 q^{-8} -36 q^{-9} -553 q^{-10} -19 q^{-11} +546 q^{-12} +67 q^{-13} -510 q^{-14} -105 q^{-15} +452 q^{-16} +124 q^{-17} -373 q^{-18} -130 q^{-19} +293 q^{-20} +114 q^{-21} -213 q^{-22} -91 q^{-23} +146 q^{-24} +66 q^{-25} -97 q^{-26} -40 q^{-27} +59 q^{-28} +24 q^{-29} -36 q^{-30} -12 q^{-31} +20 q^{-32} +6 q^{-33} -11 q^{-34} - q^{-35} +3 q^{-36} +2 q^{-37} -3 q^{-38} + q^{-39} } |
| 4 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{36}-3 q^{35}+5 q^{33}+6 q^{31}-20 q^{30}-10 q^{29}+20 q^{28}+15 q^{27}+48 q^{26}-64 q^{25}-73 q^{24}+8 q^{23}+45 q^{22}+206 q^{21}-67 q^{20}-196 q^{19}-141 q^{18}-28 q^{17}+507 q^{16}+119 q^{15}-231 q^{14}-445 q^{13}-398 q^{12}+757 q^{11}+517 q^{10}+69 q^9-692 q^8-1095 q^7+682 q^6+898 q^5+746 q^4-604 q^3-1864 q^2+210 q+981+1579 q^{-1} -122 q^{-2} -2422 q^{-3} -475 q^{-4} +713 q^{-5} +2302 q^{-6} +577 q^{-7} -2665 q^{-8} -1157 q^{-9} +235 q^{-10} +2791 q^{-11} +1288 q^{-12} -2619 q^{-13} -1710 q^{-14} -320 q^{-15} +2980 q^{-16} +1883 q^{-17} -2279 q^{-18} -2026 q^{-19} -874 q^{-20} +2774 q^{-21} +2217 q^{-22} -1656 q^{-23} -1940 q^{-24} -1285 q^{-25} +2135 q^{-26} +2127 q^{-27} -916 q^{-28} -1432 q^{-29} -1359 q^{-30} +1293 q^{-31} +1608 q^{-32} -361 q^{-33} -749 q^{-34} -1057 q^{-35} +600 q^{-36} +929 q^{-37} -119 q^{-38} -235 q^{-39} -609 q^{-40} +230 q^{-41} +409 q^{-42} -74 q^{-43} -12 q^{-44} -266 q^{-45} +91 q^{-46} +144 q^{-47} -63 q^{-48} +27 q^{-49} -92 q^{-50} +41 q^{-51} +44 q^{-52} -37 q^{-53} +16 q^{-54} -26 q^{-55} +14 q^{-56} +12 q^{-57} -13 q^{-58} +5 q^{-59} -5 q^{-60} +3 q^{-61} +2 q^{-62} -3 q^{-63} + q^{-64} } |
| 5 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{55}-3 q^{54}+5 q^{52}-q^{49}-13 q^{48}-10 q^{47}+20 q^{46}+24 q^{45}+15 q^{44}-3 q^{43}-57 q^{42}-73 q^{41}-3 q^{40}+98 q^{39}+136 q^{38}+81 q^{37}-98 q^{36}-274 q^{35}-231 q^{34}+48 q^{33}+388 q^{32}+488 q^{31}+156 q^{30}-440 q^{29}-822 q^{28}-557 q^{27}+309 q^{26}+1162 q^{25}+1143 q^{24}+98 q^{23}-1294 q^{22}-1893 q^{21}-890 q^{20}+1169 q^{19}+2580 q^{18}+1963 q^{17}-495 q^{16}-3034 q^{15}-3320 q^{14}-616 q^{13}+3036 q^{12}+4575 q^{11}+2290 q^{10}-2444 q^9-5669 q^8-4183 q^7+1215 q^6+6215 q^5+6272 q^4+563 q^3-6309 q^2-8086 q-2747+5675 q^{-1} +9762 q^{-2} +5110 q^{-3} -4708 q^{-4} -10866 q^{-5} -7467 q^{-6} +3196 q^{-7} +11732 q^{-8} +9709 q^{-9} -1663 q^{-10} -12094 q^{-11} -11696 q^{-12} -108 q^{-13} +12281 q^{-14} +13474 q^{-15} +1751 q^{-16} -12163 q^{-17} -14968 q^{-18} -3440 q^{-19} +11872 q^{-20} +16226 q^{-21} +5044 q^{-22} -11311 q^{-23} -17182 q^{-24} -6620 q^{-25} +10462 q^{-26} +17727 q^{-27} +8139 q^{-28} -9242 q^{-29} -17800 q^{-30} -9471 q^{-31} +7641 q^{-32} +17257 q^{-33} +10522 q^{-34} -5751 q^{-35} -16046 q^{-36} -11104 q^{-37} +3685 q^{-38} +14226 q^{-39} +11134 q^{-40} -1751 q^{-41} -11907 q^{-42} -10492 q^{-43} +49 q^{-44} +9366 q^{-45} +9335 q^{-46} +1143 q^{-47} -6881 q^{-48} -7734 q^{-49} -1824 q^{-50} +4654 q^{-51} +6007 q^{-52} +2020 q^{-53} -2896 q^{-54} -4354 q^{-55} -1827 q^{-56} +1630 q^{-57} +2906 q^{-58} +1475 q^{-59} -813 q^{-60} -1829 q^{-61} -1041 q^{-62} +366 q^{-63} +1045 q^{-64} +667 q^{-65} -136 q^{-66} -563 q^{-67} -378 q^{-68} +44 q^{-69} +279 q^{-70} +195 q^{-71} -23 q^{-72} -131 q^{-73} -73 q^{-74} +8 q^{-75} +49 q^{-76} +40 q^{-77} -15 q^{-78} -33 q^{-79} +5 q^{-80} +11 q^{-81} -4 q^{-82} +11 q^{-83} -5 q^{-84} -15 q^{-85} +10 q^{-86} +6 q^{-87} -7 q^{-88} +3 q^{-89} + q^{-90} -5 q^{-91} +3 q^{-92} +2 q^{-93} -3 q^{-94} + q^{-95} } |
| 6 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{78}-3 q^{77}+5 q^{75}-7 q^{72}+6 q^{71}-13 q^{70}-10 q^{69}+29 q^{68}+15 q^{67}+15 q^{66}-27 q^{65}+4 q^{64}-68 q^{63}-73 q^{62}+62 q^{61}+89 q^{60}+135 q^{59}+9 q^{58}+63 q^{57}-242 q^{56}-367 q^{55}-95 q^{54}+110 q^{53}+456 q^{52}+367 q^{51}+601 q^{50}-255 q^{49}-953 q^{48}-932 q^{47}-608 q^{46}+398 q^{45}+974 q^{44}+2312 q^{43}+1026 q^{42}-733 q^{41}-2167 q^{40}-2865 q^{39}-1764 q^{38}-12 q^{37}+4402 q^{36}+4486 q^{35}+2707 q^{34}-1036 q^{33}-5025 q^{32}-6815 q^{31}-5672 q^{30}+2853 q^{29}+7427 q^{28}+9801 q^{27}+6133 q^{26}-1711 q^{25}-10728 q^{24}-15749 q^{23}-6530 q^{22}+3169 q^{21}+14993 q^{20}+18223 q^{19}+11488 q^{18}-5657 q^{17}-23111 q^{16}-21653 q^{15}-12620 q^{14}+9494 q^{13}+26828 q^{12}+31357 q^{11}+12391 q^{10}-18421 q^9-33135 q^8-35689 q^7-10156 q^6+22642 q^5+47836 q^4+38313 q^3+1043 q^2-32044 q-55786-38220 q^{-1} +3894 q^{-2} +52563 q^{-3} +62043 q^{-4} +29106 q^{-5} -17439 q^{-6} -65382 q^{-7} -65037 q^{-8} -22978 q^{-9} +45146 q^{-10} +76917 q^{-11} +56713 q^{-12} +4383 q^{-13} -64503 q^{-14} -84666 q^{-15} -49669 q^{-16} +31243 q^{-17} +83078 q^{-18} +78682 q^{-19} +26256 q^{-20} -57964 q^{-21} -97096 q^{-22} -71826 q^{-23} +16414 q^{-24} +84162 q^{-25} +94960 q^{-26} +45142 q^{-27} -49560 q^{-28} -104730 q^{-29} -89622 q^{-30} +1943 q^{-31} +82006 q^{-32} +107014 q^{-33} +62045 q^{-34} -38712 q^{-35} -107583 q^{-36} -104025 q^{-37} -14318 q^{-38} +74179 q^{-39} +113419 q^{-40} +77868 q^{-41} -22271 q^{-42} -101680 q^{-43} -112526 q^{-44} -33077 q^{-45} +56857 q^{-46} +109001 q^{-47} +89073 q^{-48} -124 q^{-49} -82953 q^{-50} -109059 q^{-51} -49394 q^{-52} +30992 q^{-53} +89805 q^{-54} +88627 q^{-55} +21109 q^{-56} -53732 q^{-57} -90038 q^{-58} -55055 q^{-59} +4988 q^{-60} +59611 q^{-61} +73183 q^{-62} +32174 q^{-63} -24051 q^{-64} -60527 q^{-65} -46714 q^{-66} -11158 q^{-67} +29527 q^{-68} +48458 q^{-69} +29880 q^{-70} -4180 q^{-71} -31958 q^{-72} -30078 q^{-73} -14530 q^{-74} +9323 q^{-75} +25188 q^{-76} +19731 q^{-77} +3455 q^{-78} -12899 q^{-79} -14492 q^{-80} -10274 q^{-81} +543 q^{-82} +10205 q^{-83} +9688 q^{-84} +3611 q^{-85} -3947 q^{-86} -5031 q^{-87} -5025 q^{-88} -1321 q^{-89} +3269 q^{-90} +3610 q^{-91} +1822 q^{-92} -997 q^{-93} -1077 q^{-94} -1814 q^{-95} -920 q^{-96} +891 q^{-97} +1025 q^{-98} +595 q^{-99} -302 q^{-100} +10 q^{-101} -487 q^{-102} -392 q^{-103} +249 q^{-104} +219 q^{-105} +123 q^{-106} -142 q^{-107} +128 q^{-108} -92 q^{-109} -132 q^{-110} +83 q^{-111} +36 q^{-112} +12 q^{-113} -70 q^{-114} +67 q^{-115} -10 q^{-116} -40 q^{-117} +29 q^{-118} +3 q^{-119} +2 q^{-120} -26 q^{-121} +21 q^{-122} +2 q^{-123} -13 q^{-124} +9 q^{-125} - q^{-126} + q^{-127} -5 q^{-128} +3 q^{-129} +2 q^{-130} -3 q^{-131} + q^{-132} } |
| 7 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{105}-3 q^{104}+5 q^{102}-7 q^{99}+6 q^{97}-13 q^{96}-q^{95}+20 q^{94}+15 q^{93}+15 q^{92}-27 q^{91}-31 q^{90}+4 q^{89}-57 q^{88}-19 q^{87}+53 q^{86}+89 q^{85}+148 q^{84}+8 q^{83}-88 q^{82}-83 q^{81}-269 q^{80}-229 q^{79}-34 q^{78}+170 q^{77}+605 q^{76}+500 q^{75}+218 q^{74}+6 q^{73}-756 q^{72}-1064 q^{71}-1000 q^{70}-557 q^{69}+908 q^{68}+1732 q^{67}+1973 q^{66}+1827 q^{65}-112 q^{64}-1965 q^{63}-3479 q^{62}-4216 q^{61}-1785 q^{60}+1249 q^{59}+4471 q^{58}+7157 q^{57}+5569 q^{56}+1829 q^{55}-3848 q^{54}-10138 q^{53}-10979 q^{52}-7761 q^{51}-50 q^{50}+10960 q^{49}+16620 q^{48}+16829 q^{47}+8893 q^{46}-7103 q^{45}-20157 q^{44}-27579 q^{43}-22959 q^{42}-3654 q^{41}+17772 q^{40}+36288 q^{39}+40873 q^{38}+23044 q^{37}-5655 q^{36}-38811 q^{35}-58918 q^{34}-49299 q^{33}-18218 q^{32}+29217 q^{31}+70628 q^{30}+79120 q^{29}+54279 q^{28}-4146 q^{27}-70199 q^{26}-105251 q^{25}-98015 q^{24}-37985 q^{23}+50949 q^{22}+120100 q^{21}+143664 q^{20}+94365 q^{19}-10861 q^{18}-116323 q^{17}-181668 q^{16}-158894 q^{15}-49939 q^{14}+89082 q^{13}+204314 q^{12}+223127 q^{11}+125841 q^{10}-37376 q^9-204535 q^8-278016 q^7-209941 q^6-35602 q^5+180193 q^4+315818 q^3+292537 q^2+123886 q-131266-332406 q^{-1} -366700 q^{-2} -219039 q^{-3} +63541 q^{-4} +326287 q^{-5} +425090 q^{-6} +313588 q^{-7} +18020 q^{-8} -300224 q^{-9} -466762 q^{-10} -400552 q^{-11} -104271 q^{-12} +258719 q^{-13} +489935 q^{-14} +475838 q^{-15} +190604 q^{-16} -207640 q^{-17} -499106 q^{-18} -537948 q^{-19} -270228 q^{-20} +153051 q^{-21} +496546 q^{-22} +586987 q^{-23} +341870 q^{-24} -99047 q^{-25} -487955 q^{-26} -625688 q^{-27} -403628 q^{-28} +49238 q^{-29} +476008 q^{-30} +656253 q^{-31} +457319 q^{-32} -3979 q^{-33} -463670 q^{-34} -681906 q^{-35} -504643 q^{-36} -37239 q^{-37} +451185 q^{-38} +704227 q^{-39} +548224 q^{-40} +76868 q^{-41} -437224 q^{-42} -723423 q^{-43} -590117 q^{-44} -118240 q^{-45} +418986 q^{-46} +738229 q^{-47} +630766 q^{-48} +163718 q^{-49} -392270 q^{-50} -744700 q^{-51} -669088 q^{-52} -215267 q^{-53} +353345 q^{-54} +738647 q^{-55} +701339 q^{-56} +271792 q^{-57} -299629 q^{-58} -714860 q^{-59} -722203 q^{-60} -329990 q^{-61} +231138 q^{-62} +669613 q^{-63} +725758 q^{-64} +384010 q^{-65} -151130 q^{-66} -602189 q^{-67} -706850 q^{-68} -426152 q^{-69} +66032 q^{-70} +514775 q^{-71} +662652 q^{-72} +450056 q^{-73} +15962 q^{-74} -414116 q^{-75} -594816 q^{-76} -450571 q^{-77} -85577 q^{-78} +308775 q^{-79} +507937 q^{-80} +426833 q^{-81} +136688 q^{-82} -208698 q^{-83} -411023 q^{-84} -382051 q^{-85} -165017 q^{-86} +122682 q^{-87} +313046 q^{-88} +322316 q^{-89} +171536 q^{-90} -55721 q^{-91} -223315 q^{-92} -256327 q^{-93} -160059 q^{-94} +10073 q^{-95} +148231 q^{-96} +191585 q^{-97} +136538 q^{-98} +16367 q^{-99} -90360 q^{-100} -134545 q^{-101} -108038 q^{-102} -27646 q^{-103} +50119 q^{-104} +88736 q^{-105} +79332 q^{-106} +28709 q^{-107} -24306 q^{-108} -54708 q^{-109} -54676 q^{-110} -24540 q^{-111} +9734 q^{-112} +31648 q^{-113} +35373 q^{-114} +18291 q^{-115} -2489 q^{-116} -17000 q^{-117} -21548 q^{-118} -12382 q^{-119} -548 q^{-120} +8471 q^{-121} +12522 q^{-122} +7721 q^{-123} +1268 q^{-124} -3923 q^{-125} -6875 q^{-126} -4360 q^{-127} -1171 q^{-128} +1531 q^{-129} +3622 q^{-130} +2379 q^{-131} +852 q^{-132} -574 q^{-133} -1911 q^{-134} -1089 q^{-135} -426 q^{-136} +73 q^{-137} +862 q^{-138} +505 q^{-139} +325 q^{-140} +31 q^{-141} -530 q^{-142} -169 q^{-143} -48 q^{-144} -66 q^{-145} +162 q^{-146} +27 q^{-147} +107 q^{-148} +71 q^{-149} -168 q^{-150} -3 q^{-151} +32 q^{-152} -28 q^{-153} +24 q^{-154} -36 q^{-155} +34 q^{-156} +38 q^{-157} -58 q^{-158} +8 q^{-159} +18 q^{-160} -5 q^{-161} +4 q^{-162} -19 q^{-163} +10 q^{-164} +13 q^{-165} -17 q^{-166} +3 q^{-167} +5 q^{-168} - q^{-169} + q^{-170} -5 q^{-171} +3 q^{-172} +2 q^{-173} -3 q^{-174} + q^{-175} } |
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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