10 94

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^4+4 t^3-9 t^2+14 t-15+14 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }
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^8-4 z^6-5 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^7-3 q^6+6 q^5-9 q^4+11 q^3-12 q^2+11 q-8+6 q^{-1} -3 q^{-2} + q^{-3} }
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^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-12 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2-4 a^{-2} +2 a^{-4} +3}
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 2 z^9 a^{-1} +2 z^9 a^{-3} +9 z^8 a^{-2} +5 z^8 a^{-4} +4 z^8+3 a z^7+3 z^7 a^{-3} +6 z^7 a^{-5} +a^2 z^6-27 z^6 a^{-2} -9 z^6 a^{-4} +5 z^6 a^{-6} -12 z^6-9 a z^5-11 z^5 a^{-1} -15 z^5 a^{-3} -10 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+31 z^4 a^{-2} +10 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +11 z^4+6 a z^3+10 z^3 a^{-1} +16 z^3 a^{-3} +9 z^3 a^{-5} -3 z^3 a^{-7} +2 a^2 z^2-18 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} -7 z^2-a z-3 z a^{-1} -5 z a^{-3} -3 z a^{-5} +4 a^{-2} +2 a^{-4} +3}
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^8-q^6+2 q^4+1+2 q^{-2} -3 q^{-4} +2 q^{-6} -3 q^{-8} + q^{-10} - q^{-14} +2 q^{-16} - q^{-18} + q^{-20} }
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^{46}-2 q^{44}+5 q^{42}-9 q^{40}+10 q^{38}-9 q^{36}+17 q^{32}-34 q^{30}+51 q^{28}-55 q^{26}+35 q^{24}+5 q^{22}-60 q^{20}+111 q^{18}-124 q^{16}+97 q^{14}-28 q^{12}-55 q^{10}+125 q^8-149 q^6+116 q^4-36 q^2-49+109 q^{-2} -110 q^{-4} +59 q^{-6} +24 q^{-8} -87 q^{-10} +112 q^{-12} -89 q^{-14} +15 q^{-16} +69 q^{-18} -141 q^{-20} +167 q^{-22} -135 q^{-24} +54 q^{-26} +49 q^{-28} -143 q^{-30} +185 q^{-32} -173 q^{-34} +99 q^{-36} -95 q^{-40} +144 q^{-42} -127 q^{-44} +62 q^{-46} +25 q^{-48} -86 q^{-50} +94 q^{-52} -53 q^{-54} -19 q^{-56} +84 q^{-58} -110 q^{-60} +97 q^{-62} -39 q^{-64} -29 q^{-66} +84 q^{-68} -109 q^{-70} +99 q^{-72} -63 q^{-74} +18 q^{-76} +23 q^{-78} -53 q^{-80} +65 q^{-82} -58 q^{-84} +44 q^{-86} -20 q^{-88} -2 q^{-90} +17 q^{-92} -28 q^{-94} +26 q^{-96} -19 q^{-98} +11 q^{-100} -2 q^{-102} -3 q^{-104} +5 q^{-106} -6 q^{-108} +4 q^{-110} -2 q^{-112} + q^{-114} }

Further Quantum Invariants

Further quantum knot invariants for 10_94.

A1 Invariants.

Weight	Invariant
1	$q^{7}-2q^{5}+3q^{3}-2q+3q^{-1}-q^{-3}-q^{-5}+2q^{-7}-3q^{-9}+3q^{-11}-2q^{-13}+q^{-15}$
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^{22}-2 q^{20}-q^{18}+8 q^{16}-4 q^{14}-11 q^{12}+15 q^{10}+3 q^8-22 q^6+12 q^4+15 q^2-21+3 q^{-2} +18 q^{-4} -12 q^{-6} -8 q^{-8} +12 q^{-10} +5 q^{-12} -14 q^{-14} -2 q^{-16} +21 q^{-18} -12 q^{-20} -15 q^{-22} +23 q^{-24} -4 q^{-26} -15 q^{-28} +13 q^{-30} -7 q^{-34} +5 q^{-36} -2 q^{-40} + q^{-42} }
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^{45}-2 q^{43}-q^{41}+4 q^{39}+5 q^{37}-7 q^{35}-16 q^{33}+8 q^{31}+32 q^{29}+3 q^{27}-47 q^{25}-30 q^{23}+56 q^{21}+63 q^{19}-43 q^{17}-98 q^{15}+9 q^{13}+117 q^{11}+36 q^9-116 q^7-76 q^5+94 q^3+110 q-61 q^{-1} -123 q^{-3} +31 q^{-5} +123 q^{-7} - q^{-9} -117 q^{-11} -20 q^{-13} +99 q^{-15} +46 q^{-17} -81 q^{-19} -69 q^{-21} +51 q^{-23} +91 q^{-25} -11 q^{-27} -109 q^{-29} -35 q^{-31} +113 q^{-33} +79 q^{-35} -96 q^{-37} -111 q^{-39} +64 q^{-41} +122 q^{-43} -28 q^{-45} -106 q^{-47} -3 q^{-49} +77 q^{-51} +17 q^{-53} -45 q^{-55} -16 q^{-57} +20 q^{-59} +9 q^{-61} -9 q^{-63} -2 q^{-65} +6 q^{-67} -2 q^{-69} -3 q^{-71} + q^{-73} +2 q^{-75} -2 q^{-79} + q^{-81} }
4	$q^{76}-2q^{74}-q^{72}+4q^{70}+q^{68}+2q^{66}-13q^{64}-10q^{62}+17q^{60}+22q^{58}+29q^{56}-41q^{54}-79q^{52}-18q^{50}+60q^{48}+164q^{46}+38q^{44}-156q^{42}-215q^{40}-101q^{38}+278q^{36}+340q^{34}+67q^{32}-328q^{30}-527q^{28}-29q^{26}+471q^{24}+589q^{22}+79q^{20}-698q^{18}-636q^{16}+12q^{14}+791q^{12}+756q^{10}-240q^{8}-880q^{6}-681q^{4}+394q^{2}+1041+402q^{-2}-578q^{-4}-980q^{-6}-138q^{-8}+824q^{-10}+691q^{-12}-177q^{-14}-848q^{-16}-380q^{-18}+499q^{-20}+668q^{-22}+41q^{-24}-627q^{-26}-454q^{-28}+244q^{-30}+638q^{-32}+245q^{-34}-415q^{-36}-611q^{-38}-139q^{-40}+587q^{-42}+625q^{-44}+22q^{-46}-736q^{-48}-738q^{-50}+229q^{-52}+902q^{-54}+693q^{-56}-433q^{-58}-1120q^{-60}-423q^{-62}+624q^{-64}+1076q^{-66}+207q^{-68}-836q^{-70}-766q^{-72}-10q^{-74}+770q^{-76}+534q^{-78}-215q^{-80}-501q^{-82}-324q^{-84}+222q^{-86}+341q^{-88}+90q^{-90}-104q^{-92}-211q^{-94}-20q^{-96}+81q^{-98}+61q^{-100}+34q^{-102}-55q^{-104}-19q^{-106}-3q^{-108}+2q^{-110}+23q^{-112}-8q^{-114}+q^{-116}-2q^{-118}-5q^{-120}+5q^{-122}-2q^{-124}+2q^{-126}-2q^{-130}+q^{-132}$
5	$q^{115}-2q^{113}-q^{111}+4q^{109}+q^{107}-2q^{105}-4q^{103}-7q^{101}-2q^{99}+20q^{97}+29q^{95}+3q^{93}-35q^{91}-70q^{89}-57q^{87}+29q^{85}+153q^{83}+182q^{81}+47q^{79}-189q^{77}-377q^{75}-304q^{73}+77q^{71}+555q^{69}+716q^{67}+315q^{65}-473q^{63}-1126q^{61}-1045q^{59}-73q^{57}+1238q^{55}+1851q^{53}+1128q^{51}-637q^{49}-2308q^{47}-2492q^{45}-736q^{43}+1933q^{41}+3540q^{39}+2665q^{37}-437q^{35}-3709q^{33}-4540q^{31}-1916q^{29}+2582q^{27}+5605q^{25}+4549q^{23}-253q^{21}-5375q^{19}-6677q^{17}-2714q^{15}+3787q^{13}+7675q^{11}+5543q^{9}-1226q^{7}-7321q^{5}-7597q^{3}-1582q+5857q^{-1}+8459q^{-3}+3990q^{-5}-3761q^{-7}-8193q^{-9}-5571q^{-11}+1674q^{-13}+7126q^{-15}+6149q^{-17}-10q^{-19}-5670q^{-21}-5959q^{-23}-1021q^{-25}+4337q^{-27}+5278q^{-29}+1421q^{-31}-3286q^{-33}-4535q^{-35}-1499q^{-37}+2679q^{-39}+4036q^{-41}+1513q^{-43}-2314q^{-45}-3909q^{-47}-1884q^{-49}+1935q^{-51}+4143q^{-53}+2769q^{-55}-1183q^{-57}-4446q^{-59}-4162q^{-61}-249q^{-63}+4388q^{-65}+5821q^{-67}+2395q^{-69}-3569q^{-71}-7183q^{-73}-4998q^{-75}+1740q^{-77}+7677q^{-79}+7530q^{-81}+910q^{-83}-6921q^{-85}-9239q^{-87}-3829q^{-89}+4883q^{-91}+9579q^{-93}+6295q^{-95}-2085q^{-97}-8438q^{-99}-7586q^{-101}-702q^{-103}+6134q^{-105}+7465q^{-107}+2787q^{-109}-3470q^{-111}-6159q^{-113}-3707q^{-115}+1141q^{-117}+4233q^{-119}+3573q^{-121}+401q^{-123}-2380q^{-125}-2774q^{-127}-1047q^{-129}+987q^{-131}+1771q^{-133}+1086q^{-135}-177q^{-137}-952q^{-139}-819q^{-141}-142q^{-143}+408q^{-145}+490q^{-147}+214q^{-149}-121q^{-151}-261q^{-153}-163q^{-155}+16q^{-157}+108q^{-159}+92q^{-161}+23q^{-163}-38q^{-165}-49q^{-167}-17q^{-169}+16q^{-171}+14q^{-173}+6q^{-175}+2q^{-177}-7q^{-179}-5q^{-181}+3q^{-183}+2q^{-185}-2q^{-187}+2q^{-189}-2q^{-193}+q^{-195}$
6	$q^{162}-2q^{160}-q^{158}+4q^{156}+q^{154}-2q^{152}-8q^{150}+2q^{148}+q^{146}+q^{144}+26q^{142}+16q^{140}-10q^{138}-57q^{136}-51q^{134}-36q^{132}+11q^{130}+143q^{128}+195q^{126}+137q^{124}-99q^{122}-287q^{120}-459q^{118}-410q^{116}+68q^{114}+640q^{112}+1060q^{110}+830q^{108}+173q^{106}-1009q^{104}-2023q^{102}-1941q^{100}-678q^{98}+1463q^{96}+3152q^{94}+3780q^{92}+2018q^{90}-1481q^{88}-4878q^{86}-6262q^{84}-4220q^{82}+439q^{80}+6485q^{78}+9698q^{76}+7976q^{74}+1368q^{72}-7280q^{70}-13406q^{68}-13474q^{66}-5098q^{64}+7203q^{62}+17621q^{60}+19672q^{58}+11084q^{56}-5308q^{54}-21775q^{52}-27401q^{50}-18674q^{48}+2279q^{46}+24627q^{44}+36206q^{42}+28037q^{40}+1933q^{38}-27631q^{36}-44995q^{34}-37534q^{32}-7434q^{30}+30828q^{28}+54032q^{26}+46625q^{24}+11390q^{22}-34009q^{20}-61963q^{18}-54770q^{16}-13037q^{14}+38452q^{12}+68727q^{10}+58848q^{8}+12048q^{6}-43438q^{4}-73984q^{2}-58407-6957q^{-2}+49025q^{-4}+74855q^{-6}+53464q^{-8}-1068q^{-10}-54382q^{-12}-71205q^{-14}-43129q^{-16}+11182q^{-18}+56201q^{-20}+63073q^{-22}+29354q^{-24}-21399q^{-26}-54030q^{-28}-49904q^{-30}-13807q^{-32}+27979q^{-34}+47554q^{-36}+33963q^{-38}-831q^{-40}-30454q^{-42}-36637q^{-44}-17135q^{-46}+11459q^{-48}+28743q^{-50}+23642q^{-52}+2020q^{-54}-18399q^{-56}-23685q^{-58}-10475q^{-60}+9765q^{-62}+22408q^{-64}+17744q^{-66}-709q^{-68}-19502q^{-70}-25310q^{-72}-12673q^{-74}+9875q^{-76}+28391q^{-78}+29061q^{-80}+9920q^{-82}-18642q^{-84}-38325q^{-86}-34615q^{-88}-8043q^{-90}+27888q^{-92}+49828q^{-94}+42101q^{-96}+5305q^{-98}-38941q^{-100}-62377q^{-102}-48353q^{-104}-1070q^{-106}+50855q^{-108}+74553q^{-110}+51242q^{-112}-5894q^{-114}-62108q^{-116}-81915q^{-118}-50060q^{-120}+14050q^{-122}+70810q^{-124}+82726q^{-126}+43634q^{-128}-21859q^{-130}-72909q^{-132}-77196q^{-134}-34176q^{-136}+27864q^{-138}+68391q^{-140}+65402q^{-142}+23586q^{-144}-29019q^{-146}-59027q^{-148}-50902q^{-150}-13460q^{-152}+26397q^{-154}+45962q^{-156}+36219q^{-158}+6720q^{-160}-21791q^{-162}-32919q^{-164}-23055q^{-166}-2551q^{-168}+15735q^{-170}+21601q^{-172}+13820q^{-174}+60q^{-176}-10532q^{-178}-12604q^{-180}-7602q^{-182}+590q^{-184}+6519q^{-186}+7067q^{-188}+3581q^{-190}-861q^{-192}-3460q^{-194}-3688q^{-196}-1669q^{-198}+802q^{-200}+1930q^{-202}+1655q^{-204}+571q^{-206}-408q^{-208}-1035q^{-210}-799q^{-212}-100q^{-214}+329q^{-216}+448q^{-218}+281q^{-220}+68q^{-222}-216q^{-224}-242q^{-226}-70q^{-228}+29q^{-230}+84q^{-232}+70q^{-234}+54q^{-236}-36q^{-238}-53q^{-240}-11q^{-242}+10q^{-246}+4q^{-248}+16q^{-250}-6q^{-252}-10q^{-254}+3q^{-256}+2q^{-260}-2q^{-262}+2q^{-264}-2q^{-268}+q^{-270}$

A2 Invariants.

Weight	Invariant
1,0	$q^{8}-q^{6}+2q^{4}+1+2q^{-2}-3q^{-4}+2q^{-6}-3q^{-8}+q^{-10}-q^{-14}+2q^{-16}-q^{-18}+q^{-20}$
1,1	$q^{28}-4q^{26}+12q^{24}-30q^{22}+64q^{20}-112q^{18}+188q^{16}-284q^{14}+387q^{12}-482q^{10}+544q^{8}-558q^{6}+502q^{4}-366q^{2}+172+74q^{-2}-329q^{-4}+574q^{-6}-784q^{-8}+928q^{-10}-999q^{-12}+982q^{-14}-884q^{-16}+720q^{-18}-501q^{-20}+264q^{-22}-30q^{-24}-162q^{-26}+302q^{-28}-386q^{-30}+414q^{-32}-404q^{-34}+367q^{-36}-320q^{-38}+268q^{-40}-218q^{-42}+171q^{-44}-128q^{-46}+92q^{-48}-60q^{-50}+36q^{-52}-20q^{-54}+10q^{-56}-4q^{-58}+q^{-60}$
2,0	$q^{24}-q^{22}-q^{20}+4q^{18}+2q^{16}-4q^{14}+6q^{10}-9q^{6}+7q^{2}-4-6q^{-2}+9q^{-4}+q^{-6}-5q^{-8}+4q^{-10}+5q^{-12}-3q^{-14}-4q^{-16}+9q^{-18}-9q^{-22}+3q^{-24}+8q^{-26}-7q^{-28}-5q^{-30}+6q^{-32}+q^{-34}-3q^{-36}-2q^{-38}+3q^{-40}-2q^{-44}+2q^{-46}-q^{-50}+q^{-52}$

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^{20}-2 q^{18}+q^{16}+3 q^{14}-7 q^{12}+5 q^{10}+5 q^8-12 q^6+13 q^4+7 q^2-14+12 q^{-2} +7 q^{-4} -17 q^{-6} +2 q^{-8} +5 q^{-10} -9 q^{-12} -4 q^{-14} +2 q^{-16} +8 q^{-18} -7 q^{-20} -2 q^{-22} +19 q^{-24} -10 q^{-26} -8 q^{-28} +18 q^{-30} -8 q^{-32} -10 q^{-34} +12 q^{-36} -2 q^{-38} -6 q^{-40} +5 q^{-42} -2 q^{-46} + q^{-48} }
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^9-q^7+3 q^5-q^3+4 q- q^{-1} +2 q^{-3} -2 q^{-5} - q^{-7} - q^{-9} -2 q^{-11} + q^{-13} -2 q^{-15} +3 q^{-17} -2 q^{-19} +3 q^{-21} - q^{-23} + q^{-25} }
1,0,1	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^{34}-4 q^{32}+10 q^{30}-16 q^{28}+13 q^{26}+10 q^{24}-48 q^{22}+94 q^{20}-101 q^{18}+51 q^{16}+64 q^{14}-203 q^{12}+293 q^{10}-283 q^8+147 q^6+84 q^4-309 q^2+458-433 q^{-2} +260 q^{-4} -19 q^{-6} -190 q^{-8} +250 q^{-10} -205 q^{-12} +103 q^{-14} -51 q^{-16} +100 q^{-18} -192 q^{-20} +274 q^{-22} -228 q^{-24} +58 q^{-26} +191 q^{-28} -396 q^{-30} +449 q^{-32} -318 q^{-34} +64 q^{-36} +182 q^{-38} -308 q^{-40} +265 q^{-42} -109 q^{-44} -66 q^{-46} +164 q^{-48} -155 q^{-50} +67 q^{-52} +36 q^{-54} -97 q^{-56} +97 q^{-58} -49 q^{-60} -6 q^{-62} +40 q^{-64} -41 q^{-66} +22 q^{-68} -2 q^{-70} -8 q^{-72} +8 q^{-74} -4 q^{-76} + q^{-78} }

A4 Invariants.

Weight	Invariant
0,1,0,0	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^{22}-q^{20}+3 q^{16}-3 q^{14}-q^{12}+5 q^{10}-2 q^8-2 q^6+12 q^4+4 q^2-5+8 q^{-2} +11 q^{-4} -8 q^{-6} -14 q^{-8} +8 q^{-10} -2 q^{-12} -23 q^{-14} -2 q^{-16} +14 q^{-18} -14 q^{-20} -3 q^{-22} +21 q^{-24} +2 q^{-26} -7 q^{-28} +12 q^{-30} +10 q^{-32} -12 q^{-34} -5 q^{-36} +10 q^{-38} -2 q^{-40} -13 q^{-42} +5 q^{-44} +7 q^{-46} -6 q^{-48} - q^{-50} +4 q^{-52} - q^{-54} - q^{-56} + q^{-58} }
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^{10}-q^8+3 q^6+3 q^2+2+2 q^{-4} -3 q^{-6} -4 q^{-10} -3 q^{-14} + q^{-16} - q^{-18} + q^{-20} +2 q^{-22} - q^{-24} +3 q^{-26} - q^{-28} + q^{-30} }

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^{20}-2 q^{18}+5 q^{16}-9 q^{14}+13 q^{12}-17 q^{10}+21 q^8-22 q^6+23 q^4-17 q^2+12-2 q^{-2} -7 q^{-4} +19 q^{-6} -30 q^{-8} +37 q^{-10} -43 q^{-12} +42 q^{-14} -40 q^{-16} +32 q^{-18} -23 q^{-20} +12 q^{-22} - q^{-24} -8 q^{-26} +16 q^{-28} -20 q^{-30} +22 q^{-32} -20 q^{-34} +18 q^{-36} -14 q^{-38} +10 q^{-40} -7 q^{-42} +4 q^{-44} -2 q^{-46} + q^{-48} }
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^{34}-2 q^{30}-2 q^{28}+3 q^{26}+6 q^{24}-2 q^{22}-10 q^{20}-3 q^{18}+13 q^{16}+12 q^{14}-11 q^{12}-19 q^{10}+3 q^8+25 q^6+10 q^4-19 q^2-18+11 q^{-2} +22 q^{-4} + q^{-6} -20 q^{-8} -8 q^{-10} +13 q^{-12} +9 q^{-14} -11 q^{-16} -12 q^{-18} +8 q^{-20} +12 q^{-22} -6 q^{-24} -16 q^{-26} +3 q^{-28} +18 q^{-30} +3 q^{-32} -18 q^{-34} -8 q^{-36} +18 q^{-38} +16 q^{-40} -11 q^{-42} -21 q^{-44} +2 q^{-46} +22 q^{-48} +9 q^{-50} -15 q^{-52} -16 q^{-54} +3 q^{-56} +15 q^{-58} +5 q^{-60} -8 q^{-62} -8 q^{-64} + q^{-66} +6 q^{-68} +2 q^{-70} -2 q^{-72} -2 q^{-74} + q^{-78} }

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^{26}-2 q^{24}+3 q^{22}-5 q^{20}+8 q^{18}-11 q^{16}+12 q^{14}-15 q^{12}+19 q^{10}-17 q^8+19 q^6-13 q^4+18 q^2-6+6 q^{-2} +3 q^{-4} -6 q^{-6} +11 q^{-8} -24 q^{-10} +21 q^{-12} -32 q^{-14} +28 q^{-16} -38 q^{-18} +30 q^{-20} -30 q^{-22} +30 q^{-24} -21 q^{-26} +18 q^{-28} -8 q^{-30} +9 q^{-32} +5 q^{-34} -7 q^{-36} +9 q^{-38} -14 q^{-40} +18 q^{-42} -17 q^{-44} +13 q^{-46} -16 q^{-48} +15 q^{-50} -10 q^{-52} +8 q^{-54} -8 q^{-56} +6 q^{-58} -3 q^{-60} +2 q^{-62} -2 q^{-64} + q^{-66} }

G2 Invariants.

Weight

Invariant

1,0

$q^{46}-2q^{44}+5q^{42}-9q^{40}+10q^{38}-9q^{36}+17q^{32}-34q^{30}+51q^{28}-55q^{26}+35q^{24}+5q^{22}-60q^{20}+111q^{18}-124q^{16}+97q^{14}-28q^{12}-55q^{10}+125q^{8}-149q^{6}+116q^{4}-36q^{2}-49+109q^{-2}-110q^{-4}+59q^{-6}+24q^{-8}-87q^{-10}+112q^{-12}-89q^{-14}+15q^{-16}+69q^{-18}-141q^{-20}+167q^{-22}-135q^{-24}+54q^{-26}+49q^{-28}-143q^{-30}+185q^{-32}-173q^{-34}+99q^{-36}-95q^{-40}+144q^{-42}-127q^{-44}+62q^{-46}+25q^{-48}-86q^{-50}+94q^{-52}-53q^{-54}-19q^{-56}+84q^{-58}-110q^{-60}+97q^{-62}-39q^{-64}-29q^{-66}+84q^{-68}-109q^{-70}+99q^{-72}-63q^{-74}+18q^{-76}+23q^{-78}-53q^{-80}+65q^{-82}-58q^{-84}+44q^{-86}-20q^{-88}-2q^{-90}+17q^{-92}-28q^{-94}+26q^{-96}-19q^{-98}+11q^{-100}-2q^{-102}-3q^{-104}+5q^{-106}-6q^{-108}+4q^{-110}-2q^{-112}+q^{-114}$

.

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 94"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[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 -t^4+4 t^3-9 t^2+14 t-15+14 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-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 -z^8-4 z^6-5 z^4-2 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]=

{ 71, 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^7-3 q^6+6 q^5-9 q^4+11 q^3-12 q^2+11 q-8+6 q^{-1} -3 q^{-2} + q^{-3} }

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^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-12 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2-4 a^{-2} +2 a^{-4} +3}

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 2 z^9 a^{-1} +2 z^9 a^{-3} +9 z^8 a^{-2} +5 z^8 a^{-4} +4 z^8+3 a z^7+3 z^7 a^{-3} +6 z^7 a^{-5} +a^2 z^6-27 z^6 a^{-2} -9 z^6 a^{-4} +5 z^6 a^{-6} -12 z^6-9 a z^5-11 z^5 a^{-1} -15 z^5 a^{-3} -10 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+31 z^4 a^{-2} +10 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +11 z^4+6 a z^3+10 z^3 a^{-1} +16 z^3 a^{-3} +9 z^3 a^{-5} -3 z^3 a^{-7} +2 a^2 z^2-18 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} -7 z^2-a z-3 z a^{-1} -5 z a^{-3} -3 z a^{-5} +4 a^{-2} +2 a^{-4} +3}