10 77

From Knot Atlas
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Polynomial invariants

Alexander polynomial
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 2 z^6+5 z^4+4 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 { 63, 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^8+3 q^7-6 q^6+8 q^5-10 q^4+11 q^3-9 q^2+8 q-4+2 q^{-1} - q^{-2} }
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^6 a^{-2} +z^6 a^{-4} +4 z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -z^4+7 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} -3 z^2+5 a^{-2} - a^{-4} - a^{-6} -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 z^9 a^{-3} +z^9 a^{-5} +2 z^8 a^{-2} +5 z^8 a^{-4} +3 z^8 a^{-6} +2 z^7 a^{-1} +2 z^7 a^{-3} +4 z^7 a^{-5} +4 z^7 a^{-7} -z^6 a^{-2} -9 z^6 a^{-4} -3 z^6 a^{-6} +3 z^6 a^{-8} +2 z^6+a z^5-z^5 a^{-1} -3 z^5 a^{-3} -9 z^5 a^{-5} -7 z^5 a^{-7} +z^5 a^{-9} -3 z^4 a^{-2} +8 z^4 a^{-4} -6 z^4 a^{-8} -5 z^4-3 a z^3-5 z^3 a^{-1} +6 z^3 a^{-5} +2 z^3 a^{-7} -2 z^3 a^{-9} +7 z^2 a^{-2} -z^2 a^{-4} -2 z^2 a^{-6} +2 z^2 a^{-8} +4 z^2+2 a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} -z a^{-7} +z a^{-9} -5 a^{-2} - a^{-4} + a^{-6} -2}
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^6-q^2-1+3 q^{-2} +4 q^{-6} +2 q^{-8} + q^{-12} -3 q^{-14} + q^{-16} - q^{-18} - q^{-20} + q^{-22} - q^{-24} }
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^{32}-q^{30}+3 q^{28}-4 q^{26}+3 q^{24}-3 q^{22}-3 q^{20}+8 q^{18}-14 q^{16}+17 q^{14}-19 q^{12}+12 q^{10}-q^8-16 q^6+34 q^4-51 q^2+53-43 q^{-2} +11 q^{-4} +26 q^{-6} -65 q^{-8} +95 q^{-10} -88 q^{-12} +60 q^{-14} -5 q^{-16} -49 q^{-18} +88 q^{-20} -85 q^{-22} +56 q^{-24} -42 q^{-28} +65 q^{-30} -46 q^{-32} +2 q^{-34} +59 q^{-36} -95 q^{-38} +96 q^{-40} -54 q^{-42} -20 q^{-44} +95 q^{-46} -142 q^{-48} +146 q^{-50} -104 q^{-52} +28 q^{-54} +54 q^{-56} -116 q^{-58} +135 q^{-60} -109 q^{-62} +47 q^{-64} +19 q^{-66} -69 q^{-68} +78 q^{-70} -50 q^{-72} - q^{-74} +52 q^{-76} -77 q^{-78} +62 q^{-80} -17 q^{-82} -47 q^{-84} +94 q^{-86} -108 q^{-88} +84 q^{-90} -33 q^{-92} -27 q^{-94} +73 q^{-96} -90 q^{-98} +81 q^{-100} -48 q^{-102} +9 q^{-104} +20 q^{-106} -40 q^{-108} +39 q^{-110} -29 q^{-112} +17 q^{-114} -3 q^{-116} -5 q^{-118} +8 q^{-120} -8 q^{-122} +5 q^{-124} -2 q^{-126} + q^{-128} }
Further Quantum Invariants
Further quantum knot invariants for 10_77.

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^5+q^3-2 q+4 q^{-1} - q^{-3} +2 q^{-5} + q^{-7} -2 q^{-9} +2 q^{-11} -3 q^{-13} +2 q^{-15} - q^{-17} }
2
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^{33}+q^{31}+q^{29}-2 q^{25}+2 q^{23}+2 q^{21}-4 q^{19}-4 q^{17}+8 q^{15}+8 q^{13}-16 q^{11}-18 q^9+21 q^7+34 q^5-26 q^3-53 q+17 q^{-1} +83 q^{-3} -6 q^{-5} -93 q^{-7} -18 q^{-9} +103 q^{-11} +43 q^{-13} -93 q^{-15} -60 q^{-17} +75 q^{-19} +70 q^{-21} -46 q^{-23} -69 q^{-25} +16 q^{-27} +67 q^{-29} +11 q^{-31} -54 q^{-33} -47 q^{-35} +43 q^{-37} +66 q^{-39} -27 q^{-41} -92 q^{-43} +11 q^{-45} +102 q^{-47} +13 q^{-49} -104 q^{-51} -36 q^{-53} +95 q^{-55} +54 q^{-57} -73 q^{-59} -64 q^{-61} +46 q^{-63} +65 q^{-65} -20 q^{-67} -55 q^{-69} +3 q^{-71} +36 q^{-73} +8 q^{-75} -21 q^{-77} -9 q^{-79} +11 q^{-81} +5 q^{-83} -4 q^{-85} -3 q^{-87} + q^{-89} +2 q^{-91} - q^{-93} }
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^{56}-q^{54}-q^{52}-q^{48}+4 q^{46}-2 q^{44}+3 q^{40}-6 q^{38}+4 q^{36}-7 q^{34}+4 q^{32}+19 q^{30}-7 q^{28}-5 q^{26}-37 q^{24}-2 q^{22}+61 q^{20}+30 q^{18}-2 q^{16}-118 q^{14}-73 q^{12}+101 q^{10}+147 q^8+98 q^6-205 q^4-265 q^2+19+282 q^{-2} +365 q^{-4} -143 q^{-6} -484 q^{-8} -253 q^{-10} +248 q^{-12} +638 q^{-14} +125 q^{-16} -495 q^{-18} -533 q^{-20} + q^{-22} +669 q^{-24} +391 q^{-26} -266 q^{-28} -575 q^{-30} -247 q^{-32} +436 q^{-34} +454 q^{-36} +15 q^{-38} -400 q^{-40} -353 q^{-42} +127 q^{-44} +365 q^{-46} +226 q^{-48} -169 q^{-50} -366 q^{-52} -164 q^{-54} +248 q^{-56} +401 q^{-58} +54 q^{-60} -358 q^{-62} -433 q^{-64} +108 q^{-66} +535 q^{-68} +300 q^{-70} -271 q^{-72} -646 q^{-74} -116 q^{-76} +519 q^{-78} +515 q^{-80} -36 q^{-82} -661 q^{-84} -356 q^{-86} +274 q^{-88} +545 q^{-90} +251 q^{-92} -419 q^{-94} -421 q^{-96} -42 q^{-98} +329 q^{-100} +355 q^{-102} -101 q^{-104} -257 q^{-106} -184 q^{-108} +65 q^{-110} +233 q^{-112} +49 q^{-114} -56 q^{-116} -119 q^{-118} -42 q^{-120} +77 q^{-122} +36 q^{-124} +16 q^{-126} -35 q^{-128} -28 q^{-130} +17 q^{-132} +5 q^{-134} +10 q^{-136} -6 q^{-138} -8 q^{-140} +4 q^{-142} +3 q^{-146} - q^{-148} -2 q^{-150} + q^{-152} }
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^{85}+q^{83}+q^{81}+q^{77}-q^{75}-4 q^{73}+2 q^{69}-q^{67}+5 q^{65}+5 q^{63}-5 q^{61}-7 q^{59}-6 q^{57}-7 q^{55}+10 q^{53}+27 q^{51}+16 q^{49}-13 q^{47}-40 q^{45}-48 q^{43}-2 q^{41}+71 q^{39}+106 q^{37}+40 q^{35}-95 q^{33}-192 q^{31}-137 q^{29}+83 q^{27}+312 q^{25}+319 q^{23}+q^{21}-428 q^{19}-597 q^{17}-241 q^{15}+475 q^{13}+948 q^{11}+668 q^9-328 q^7-1310 q^5-1302 q^3-63 q+1503 q^{-1} +2026 q^{-3} +824 q^{-5} -1426 q^{-7} -2748 q^{-9} -1748 q^{-11} +953 q^{-13} +3162 q^{-15} +2820 q^{-17} -116 q^{-19} -3236 q^{-21} -3677 q^{-23} -899 q^{-25} +2809 q^{-27} +4208 q^{-29} +1925 q^{-31} -2061 q^{-33} -4257 q^{-35} -2715 q^{-37} +1139 q^{-39} +3861 q^{-41} +3146 q^{-43} -227 q^{-45} -3169 q^{-47} -3204 q^{-49} -520 q^{-51} +2345 q^{-53} +2963 q^{-55} +1055 q^{-57} -1535 q^{-59} -2576 q^{-61} -1397 q^{-63} +803 q^{-65} +2174 q^{-67} +1648 q^{-69} -213 q^{-71} -1814 q^{-73} -1871 q^{-75} -366 q^{-77} +1546 q^{-79} +2186 q^{-81} +883 q^{-83} -1300 q^{-85} -2505 q^{-87} -1536 q^{-89} +1021 q^{-91} +2888 q^{-93} +2206 q^{-95} -606 q^{-97} -3121 q^{-99} -2953 q^{-101} -7 q^{-103} +3176 q^{-105} +3615 q^{-107} +782 q^{-109} -2875 q^{-111} -4075 q^{-113} -1659 q^{-115} +2233 q^{-117} +4178 q^{-119} +2483 q^{-121} -1309 q^{-123} -3848 q^{-125} -3048 q^{-127} +245 q^{-129} +3108 q^{-131} +3230 q^{-133} +729 q^{-135} -2110 q^{-137} -2971 q^{-139} -1404 q^{-141} +1053 q^{-143} +2346 q^{-145} +1681 q^{-147} -151 q^{-149} -1574 q^{-151} -1564 q^{-153} -411 q^{-155} +811 q^{-157} +1185 q^{-159} +648 q^{-161} -239 q^{-163} -753 q^{-165} -594 q^{-167} -70 q^{-169} +357 q^{-171} +417 q^{-173} +184 q^{-175} -115 q^{-177} -241 q^{-179} -153 q^{-181} +5 q^{-183} +102 q^{-185} +92 q^{-187} +31 q^{-189} -35 q^{-191} -50 q^{-193} -16 q^{-195} +10 q^{-197} +15 q^{-199} +7 q^{-201} +2 q^{-203} -8 q^{-205} -6 q^{-207} +5 q^{-209} +3 q^{-211} - q^{-213} -3 q^{-219} + q^{-221} +2 q^{-223} - q^{-225} }

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^6-q^2-1+3 q^{-2} +4 q^{-6} +2 q^{-8} + q^{-12} -3 q^{-14} + q^{-16} - q^{-18} - q^{-20} + q^{-22} - q^{-24} }
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^{20}-2 q^{18}+6 q^{16}-12 q^{14}+23 q^{12}-38 q^{10}+58 q^8-92 q^6+128 q^4-182 q^2+234-300 q^{-2} +352 q^{-4} -382 q^{-6} +392 q^{-8} -338 q^{-10} +257 q^{-12} -96 q^{-14} -70 q^{-16} +282 q^{-18} -482 q^{-20} +652 q^{-22} -784 q^{-24} +832 q^{-26} -831 q^{-28} +740 q^{-30} -598 q^{-32} +410 q^{-34} -198 q^{-36} -8 q^{-38} +188 q^{-40} -324 q^{-42} +406 q^{-44} -436 q^{-46} +416 q^{-48} -360 q^{-50} +291 q^{-52} -218 q^{-54} +148 q^{-56} -92 q^{-58} +54 q^{-60} -28 q^{-62} +12 q^{-64} -4 q^{-66} + q^{-68} }
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^{18}-q^{14}+q^{12}+2 q^{10}-3 q^8-4 q^6+2 q^4+2 q^2-8-5 q^{-2} +9 q^{-4} + q^{-6} -7 q^{-8} +4 q^{-10} +12 q^{-12} +3 q^{-14} + q^{-16} +11 q^{-18} +7 q^{-20} -7 q^{-22} + q^{-26} -10 q^{-28} -7 q^{-30} +5 q^{-32} - q^{-34} -9 q^{-36} +7 q^{-40} - q^{-42} -7 q^{-44} +4 q^{-46} +5 q^{-48} -2 q^{-50} -2 q^{-52} + q^{-54} +2 q^{-56} - q^{-58} - q^{-60} + q^{-62} }

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^{14}-q^{12}+q^{10}+2 q^8-5 q^6-q^4+3 q^2-13-2 q^{-2} +14 q^{-4} -11 q^{-6} +5 q^{-8} +23 q^{-10} -4 q^{-12} +12 q^{-16} -4 q^{-18} -7 q^{-20} -2 q^{-22} +5 q^{-24} -4 q^{-26} -11 q^{-28} +11 q^{-30} + q^{-32} -17 q^{-34} +11 q^{-36} +5 q^{-38} -14 q^{-40} +8 q^{-42} +3 q^{-44} -7 q^{-46} +4 q^{-48} + q^{-50} -2 q^{-52} + q^{-54} }
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^7-2 q^3-2 q^{-1} +3 q^{-3} +5 q^{-7} +3 q^{-9} +3 q^{-11} + q^{-13} - q^{-15} -3 q^{-19} + q^{-21} -2 q^{-23} + q^{-25} -2 q^{-27} + q^{-29} - q^{-31} }

A4 Invariants.

Weight Invariant
0,1,0,0
1,0,0,0 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^8-2 q^4-q^2-1-2 q^{-2} +3 q^{-4} +5 q^{-8} +4 q^{-10} +4 q^{-12} +3 q^{-14} + q^{-16} -2 q^{-20} -3 q^{-24} + q^{-26} -2 q^{-28} -2 q^{-34} + q^{-36} - q^{-38} }

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^{14}+q^{12}-3 q^{10}+4 q^8-7 q^6+9 q^4-13 q^2+15-16 q^{-2} +18 q^{-4} -13 q^{-6} +11 q^{-8} - q^{-10} -4 q^{-12} +16 q^{-14} -22 q^{-16} +30 q^{-18} -33 q^{-20} +34 q^{-22} -33 q^{-24} +26 q^{-26} -19 q^{-28} +9 q^{-30} - q^{-32} -7 q^{-34} +13 q^{-36} -17 q^{-38} +18 q^{-40} -18 q^{-42} +15 q^{-44} -11 q^{-46} +8 q^{-48} -5 q^{-50} +2 q^{-52} - q^{-54} }
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^{24}-q^{20}-q^{18}+2 q^{16}+3 q^{14}-q^{12}-6 q^{10}-4 q^8+4 q^6+8 q^4-3 q^2-15-8 q^{-2} +11 q^{-4} +17 q^{-6} -4 q^{-8} -17 q^{-10} -3 q^{-12} +20 q^{-14} +15 q^{-16} -6 q^{-18} -12 q^{-20} +7 q^{-22} +15 q^{-24} + q^{-26} -13 q^{-28} -3 q^{-30} +10 q^{-32} +4 q^{-34} -11 q^{-36} -9 q^{-38} +8 q^{-40} +9 q^{-42} -8 q^{-44} -14 q^{-46} +4 q^{-48} +16 q^{-50} +2 q^{-52} -18 q^{-54} -12 q^{-56} +13 q^{-58} +18 q^{-60} -4 q^{-62} -18 q^{-64} -6 q^{-66} +13 q^{-68} +10 q^{-70} -5 q^{-72} -9 q^{-74} - q^{-76} +6 q^{-78} +3 q^{-80} -2 q^{-82} -2 q^{-84} + q^{-88} }

D4 Invariants.

Weight Invariant
1,0,0,0 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^{18}-q^{16}+2 q^{14}-2 q^{12}+4 q^{10}-6 q^8+4 q^6-10 q^4+7 q^2-16+8 q^{-2} -14 q^{-4} +15 q^{-6} -10 q^{-8} +13 q^{-10} + q^{-12} +13 q^{-14} +10 q^{-16} -3 q^{-18} +14 q^{-20} -14 q^{-22} +22 q^{-24} -26 q^{-26} +21 q^{-28} -29 q^{-30} +26 q^{-32} -24 q^{-34} +19 q^{-36} -20 q^{-38} +11 q^{-40} -6 q^{-42} + q^{-44} - q^{-46} -8 q^{-48} +11 q^{-50} -12 q^{-52} +13 q^{-54} -15 q^{-56} +15 q^{-58} -12 q^{-60} +10 q^{-62} -9 q^{-64} +7 q^{-66} -4 q^{-68} +3 q^{-70} -2 q^{-72} + q^{-74} }

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^{32}-q^{30}+3 q^{28}-4 q^{26}+3 q^{24}-3 q^{22}-3 q^{20}+8 q^{18}-14 q^{16}+17 q^{14}-19 q^{12}+12 q^{10}-q^8-16 q^6+34 q^4-51 q^2+53-43 q^{-2} +11 q^{-4} +26 q^{-6} -65 q^{-8} +95 q^{-10} -88 q^{-12} +60 q^{-14} -5 q^{-16} -49 q^{-18} +88 q^{-20} -85 q^{-22} +56 q^{-24} -42 q^{-28} +65 q^{-30} -46 q^{-32} +2 q^{-34} +59 q^{-36} -95 q^{-38} +96 q^{-40} -54 q^{-42} -20 q^{-44} +95 q^{-46} -142 q^{-48} +146 q^{-50} -104 q^{-52} +28 q^{-54} +54 q^{-56} -116 q^{-58} +135 q^{-60} -109 q^{-62} +47 q^{-64} +19 q^{-66} -69 q^{-68} +78 q^{-70} -50 q^{-72} - q^{-74} +52 q^{-76} -77 q^{-78} +62 q^{-80} -17 q^{-82} -47 q^{-84} +94 q^{-86} -108 q^{-88} +84 q^{-90} -33 q^{-92} -27 q^{-94} +73 q^{-96} -90 q^{-98} +81 q^{-100} -48 q^{-102} +9 q^{-104} +20 q^{-106} -40 q^{-108} +39 q^{-110} -29 q^{-112} +17 q^{-114} -3 q^{-116} -5 q^{-118} +8 q^{-120} -8 q^{-122} +5 q^{-124} -2 q^{-126} + q^{-128} }

.

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`
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.

Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:= K = Knot["10 77"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]=
In[5]:= Conway[K][z]
Out[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 2 z^6+5 z^4+4 z^2+1}
In[6]:= Alexander[K, 2][t]
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]= 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]:= {KnotDet[K], KnotSignature[K]}
Out[7]= { 63, 2 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= 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^8+3 q^7-6 q^6+8 q^5-10 q^4+11 q^3-9 q^2+8 q-4+2 q^{-1} - q^{-2} }
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= 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 a^{-2} +z^6 a^{-4} +4 z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -z^4+7 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} -3 z^2+5 a^{-2} - a^{-4} - a^{-6} -2}
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= 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^9 a^{-3} +z^9 a^{-5} +2 z^8 a^{-2} +5 z^8 a^{-4} +3 z^8 a^{-6} +2 z^7 a^{-1} +2 z^7 a^{-3} +4 z^7 a^{-5} +4 z^7 a^{-7} -z^6 a^{-2} -9 z^6 a^{-4} -3 z^6 a^{-6} +3 z^6 a^{-8} +2 z^6+a z^5-z^5 a^{-1} -3 z^5 a^{-3} -9 z^5 a^{-5} -7 z^5 a^{-7} +z^5 a^{-9} -3 z^4 a^{-2} +8 z^4 a^{-4} -6 z^4 a^{-8} -5 z^4-3 a z^3-5 z^3 a^{-1} +6 z^3 a^{-5} +2 z^3 a^{-7} -2 z^3 a^{-9} +7 z^2 a^{-2} -z^2 a^{-4} -2 z^2 a^{-6} +2 z^2 a^{-8} +4 z^2+2 a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} -z a^{-7} +z a^{-9} -5 a^{-2} - a^{-4} + a^{-6} -2}
Retrieved from "https://katlas.org/index.php?title=10_77&oldid=4609"