10 5

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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^4-3 t^3+5 t^2-5 t+5-5 t^{-1} +5 t^{-2} -3 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+5 z^6+7 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 { 33, 4 }
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^9+2 q^8-3 q^7+4 q^6-5 q^5+5 q^4-4 q^3+4 q^2-2 q+2- q^{-1} }
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^{-4} -z^6 a^{-2} +7 z^6 a^{-4} -z^6 a^{-6} -5 z^4 a^{-2} +17 z^4 a^{-4} -5 z^4 a^{-6} -6 z^2 a^{-2} +17 z^2 a^{-4} -7 z^2 a^{-6} - a^{-2} +5 a^{-4} -3 a^{-6} }
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} +4 z^8 a^{-4} +2 z^8 a^{-6} +z^7 a^{-1} -3 z^7 a^{-3} -2 z^7 a^{-5} +2 z^7 a^{-7} -11 z^6 a^{-2} -20 z^6 a^{-4} -7 z^6 a^{-6} +2 z^6 a^{-8} -5 z^5 a^{-1} -2 z^5 a^{-3} -3 z^5 a^{-5} -4 z^5 a^{-7} +2 z^5 a^{-9} +18 z^4 a^{-2} +32 z^4 a^{-4} +10 z^4 a^{-6} -2 z^4 a^{-8} +2 z^4 a^{-10} +6 z^3 a^{-1} +7 z^3 a^{-3} +6 z^3 a^{-5} +3 z^3 a^{-7} -z^3 a^{-9} +z^3 a^{-11} -10 z^2 a^{-2} -22 z^2 a^{-4} -9 z^2 a^{-6} +z^2 a^{-8} -2 z^2 a^{-10} -z a^{-1} -2 z a^{-3} -3 z a^{-5} -z a^{-7} -z a^{-11} + a^{-2} +5 a^{-4} +3 a^{-6} }
The A2 invariant
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^{12}-q^{10}+2 q^8-3 q^6+q^4-2 q^2-1+5 q^{-2} -8 q^{-4} +8 q^{-6} -7 q^{-8} +2 q^{-10} +3 q^{-12} -9 q^{-14} +10 q^{-16} -9 q^{-18} +5 q^{-20} +2 q^{-22} -4 q^{-24} +7 q^{-26} -3 q^{-28} +2 q^{-30} +4 q^{-32} -2 q^{-34} +2 q^{-36} +2 q^{-38} -2 q^{-40} +8 q^{-42} -4 q^{-44} +6 q^{-46} -2 q^{-48} - q^{-50} +7 q^{-52} -10 q^{-54} +9 q^{-56} -6 q^{-58} +2 q^{-60} +2 q^{-62} -6 q^{-64} +6 q^{-66} -5 q^{-68} +2 q^{-70} -3 q^{-74} + q^{-76} + q^{-78} -2 q^{-80} + q^{-82} - q^{-86} +2 q^{-88} -2 q^{-90} + q^{-92} + q^{-96} - q^{-98} - q^{-100} - q^{-104} +2 q^{-106} -4 q^{-108} +4 q^{-110} -3 q^{-112} - q^{-114} +2 q^{-116} -5 q^{-118} +5 q^{-120} -5 q^{-122} +3 q^{-124} - q^{-126} -2 q^{-128} +4 q^{-130} -4 q^{-132} +4 q^{-134} -2 q^{-136} + q^{-138} -2 q^{-142} +2 q^{-144} - q^{-146} + q^{-148} }
Further Quantum Invariants
Further quantum knot invariants for 10_5.

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^3+q+2 q^{-3} + q^{-7} - q^{-11} + q^{-13} - q^{-15} + q^{-17} - q^{-19} }
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^{12}-q^{10}-2 q^8+2 q^6-3 q^2+2+3 q^{-2} -2 q^{-4} + q^{-6} +3 q^{-8} +2 q^{-14} -2 q^{-18} + q^{-22} - q^{-24} - q^{-26} + q^{-28} -2 q^{-32} + q^{-34} - q^{-38} +2 q^{-40} - q^{-42} - q^{-44} +2 q^{-46} - q^{-48} - q^{-50} + q^{-52} }
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^{27}+q^{25}+2 q^{23}-3 q^{19}-2 q^{17}+4 q^{15}+3 q^{13}-4 q^{11}-6 q^9+q^7+6 q^5+2 q^3-6 q-2 q^{-1} +4 q^{-3} +5 q^{-5} - q^{-7} -2 q^{-9} +3 q^{-13} +3 q^{-15} +2 q^{-17} -2 q^{-19} -2 q^{-21} +2 q^{-23} +4 q^{-25} -2 q^{-27} -5 q^{-29} +2 q^{-31} +3 q^{-33} -3 q^{-35} -6 q^{-37} +3 q^{-39} +4 q^{-41} -5 q^{-45} - q^{-47} +2 q^{-49} +3 q^{-51} + q^{-53} -5 q^{-55} -4 q^{-57} +4 q^{-59} +6 q^{-61} - q^{-63} -7 q^{-65} - q^{-67} +7 q^{-69} +3 q^{-71} -5 q^{-73} -4 q^{-75} +3 q^{-77} +5 q^{-79} -2 q^{-81} -4 q^{-83} +3 q^{-87} -2 q^{-91} + q^{-95} + q^{-97} - q^{-99} }
4
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^{75}+q^{73}+2 q^{71}-q^{67}-3 q^{65}-3 q^{63}+6 q^{59}+6 q^{57}+q^{55}-5 q^{53}-10 q^{51}-8 q^{49}+3 q^{47}+16 q^{45}+15 q^{43}+3 q^{41}-11 q^{39}-22 q^{37}-15 q^{35}+5 q^{33}+22 q^{31}+21 q^{29}+7 q^{27}-13 q^{25}-28 q^{23}-18 q^{21}+3 q^{19}+20 q^{17}+22 q^{15}+8 q^{13}-11 q^{11}-18 q^9-12 q^7+q^5+11 q^3+8 q- q^{-1} - q^{-3} +2 q^{-5} +6 q^{-7} +3 q^{-9} -8 q^{-11} -20 q^{-13} -11 q^{-15} +15 q^{-17} +35 q^{-19} +27 q^{-21} -3 q^{-23} -39 q^{-25} -45 q^{-27} -7 q^{-29} +42 q^{-31} +59 q^{-33} +27 q^{-35} -31 q^{-37} -64 q^{-39} -44 q^{-41} +15 q^{-43} +62 q^{-45} +54 q^{-47} - q^{-49} -53 q^{-51} -60 q^{-53} -19 q^{-55} +40 q^{-57} +59 q^{-59} +27 q^{-61} -28 q^{-63} -55 q^{-65} -35 q^{-67} +14 q^{-69} +47 q^{-71} +37 q^{-73} -6 q^{-75} -38 q^{-77} -32 q^{-79} +2 q^{-81} +29 q^{-83} +30 q^{-85} -4 q^{-87} -29 q^{-89} -20 q^{-91} +5 q^{-93} +25 q^{-95} +21 q^{-97} -8 q^{-99} -29 q^{-101} -20 q^{-103} +6 q^{-105} +27 q^{-107} +27 q^{-109} +8 q^{-111} -19 q^{-113} -34 q^{-115} -25 q^{-117} +3 q^{-119} +35 q^{-121} +44 q^{-123} +22 q^{-125} -25 q^{-127} -59 q^{-129} -44 q^{-131} +10 q^{-133} +59 q^{-135} +59 q^{-137} +9 q^{-139} -53 q^{-141} -67 q^{-143} -21 q^{-145} +41 q^{-147} +61 q^{-149} +24 q^{-151} -30 q^{-153} -50 q^{-155} -21 q^{-157} +26 q^{-159} +40 q^{-161} +13 q^{-163} -25 q^{-165} -30 q^{-167} -4 q^{-169} +22 q^{-171} +25 q^{-173} + q^{-175} -23 q^{-177} -22 q^{-179} +2 q^{-181} +19 q^{-183} +17 q^{-185} +2 q^{-187} -13 q^{-189} -15 q^{-191} -3 q^{-193} +8 q^{-195} +9 q^{-197} +3 q^{-199} -3 q^{-201} -5 q^{-203} -3 q^{-205} + q^{-207} +3 q^{-209} + q^{-211} - q^{-217} + q^{-219} - q^{-223} - q^{-225} + q^{-231} + q^{-233} - q^{-235} }
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^{108}-q^{106}-2 q^{104}+q^{100}+3 q^{98}+q^{96}+3 q^{94}-2 q^{92}-8 q^{90}-5 q^{88}-q^{86}+6 q^{84}+7 q^{82}+14 q^{80}+3 q^{78}-12 q^{76}-18 q^{74}-17 q^{72}-3 q^{70}+6 q^{68}+33 q^{66}+30 q^{64}+8 q^{62}-15 q^{60}-35 q^{58}-34 q^{56}-27 q^{54}+19 q^{52}+43 q^{50}+45 q^{48}+25 q^{46}-8 q^{44}-36 q^{42}-62 q^{40}-30 q^{38}+3 q^{36}+37 q^{34}+49 q^{32}+36 q^{30}+8 q^{28}-38 q^{26}-40 q^{24}-33 q^{22}-3 q^{20}+22 q^{18}+31 q^{16}+22 q^{14}-10 q^{12}-14 q^{10}-17 q^8+6 q^6+20 q^4+17 q^2-2-40 q^{-2} -43 q^{-4} -26 q^{-6} +31 q^{-8} +74 q^{-10} +75 q^{-12} +32 q^{-14} -53 q^{-16} -107 q^{-18} -109 q^{-20} -25 q^{-22} +77 q^{-24} +142 q^{-26} +136 q^{-28} +29 q^{-30} -94 q^{-32} -173 q^{-34} -136 q^{-36} -23 q^{-38} +105 q^{-40} +189 q^{-42} +143 q^{-44} +18 q^{-46} -122 q^{-48} -178 q^{-50} -139 q^{-52} -22 q^{-54} +122 q^{-56} +177 q^{-58} +131 q^{-60} +5 q^{-62} -108 q^{-64} -170 q^{-66} -137 q^{-68} -4 q^{-70} +114 q^{-72} +165 q^{-74} +113 q^{-76} +6 q^{-78} -119 q^{-80} -176 q^{-82} -100 q^{-84} +26 q^{-86} +133 q^{-88} +152 q^{-90} +85 q^{-92} -52 q^{-94} -157 q^{-96} -132 q^{-98} -31 q^{-100} +85 q^{-102} +138 q^{-104} +105 q^{-106} -10 q^{-108} -116 q^{-110} -113 q^{-112} -41 q^{-114} +49 q^{-116} +94 q^{-118} +75 q^{-120} -4 q^{-122} -76 q^{-124} -67 q^{-126} -12 q^{-128} +46 q^{-130} +61 q^{-132} +30 q^{-134} -30 q^{-136} -67 q^{-138} -45 q^{-140} +9 q^{-142} +60 q^{-144} +70 q^{-146} +38 q^{-148} -22 q^{-150} -68 q^{-152} -83 q^{-154} -48 q^{-156} +16 q^{-158} +77 q^{-160} +103 q^{-162} +75 q^{-164} +7 q^{-166} -95 q^{-168} -143 q^{-170} -115 q^{-172} -11 q^{-174} +106 q^{-176} +177 q^{-178} +153 q^{-180} +8 q^{-182} -130 q^{-184} -206 q^{-186} -148 q^{-188} -10 q^{-190} +145 q^{-192} +220 q^{-194} +132 q^{-196} -9 q^{-198} -152 q^{-200} -182 q^{-202} -116 q^{-204} +25 q^{-206} +142 q^{-208} +137 q^{-210} +79 q^{-212} -31 q^{-214} -89 q^{-216} -107 q^{-218} -53 q^{-220} +22 q^{-222} +46 q^{-224} +70 q^{-226} +41 q^{-228} +17 q^{-230} -32 q^{-232} -49 q^{-234} -40 q^{-236} -34 q^{-238} +17 q^{-240} +40 q^{-242} +57 q^{-244} +22 q^{-246} -11 q^{-248} -35 q^{-250} -53 q^{-252} -18 q^{-254} +8 q^{-256} +41 q^{-258} +30 q^{-260} +14 q^{-262} -6 q^{-264} -31 q^{-266} -18 q^{-268} -12 q^{-270} +11 q^{-272} +13 q^{-274} +13 q^{-276} +7 q^{-278} -7 q^{-280} -4 q^{-282} -11 q^{-284} - q^{-286} +5 q^{-290} +5 q^{-292} +3 q^{-296} -5 q^{-298} - q^{-300} -2 q^{-302} +3 q^{-310} - q^{-312} + q^{-314} - q^{-320} - q^{-322} + q^{-324} }

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^2+ q^{-4} +2 q^{-6} + q^{-8} +2 q^{-10} - q^{-12} + q^{-14} - q^{-22} - q^{-26} }
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^{12}-2 q^{10}+4 q^8-8 q^6+13 q^4-20 q^2+24-32 q^{-2} +30 q^{-4} -30 q^{-6} +24 q^{-8} -10 q^{-10} +6 q^{-12} +18 q^{-14} -18 q^{-16} +36 q^{-18} -36 q^{-20} +44 q^{-22} -44 q^{-24} +38 q^{-26} -35 q^{-28} +22 q^{-30} -20 q^{-32} +6 q^{-34} -4 q^{-36} -2 q^{-38} +2 q^{-40} + q^{-44} +2 q^{-48} -4 q^{-50} +5 q^{-52} -10 q^{-54} +12 q^{-56} -12 q^{-58} +13 q^{-60} -12 q^{-62} +12 q^{-64} -10 q^{-66} +7 q^{-68} -6 q^{-70} +4 q^{-72} -2 q^{-74} + q^{-76} }
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^{10}-q^6-q^4-1-3 q^{-2} +2 q^{-6} + q^{-8} +4 q^{-12} +4 q^{-14} +3 q^{-16} +2 q^{-18} +3 q^{-20} - q^{-24} - q^{-30} + q^{-34} -3 q^{-36} -3 q^{-38} - q^{-40} - q^{-44} - q^{-46} + q^{-48} + q^{-50} - q^{-54} + q^{-66} }

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^6-q^4-3 q^{-2} +2 q^{-10} +3 q^{-12} + q^{-14} +4 q^{-16} +2 q^{-18} + q^{-20} +4 q^{-22} +2 q^{-24} - q^{-26} - q^{-30} -3 q^{-32} -3 q^{-34} - q^{-36} -2 q^{-40} +2 q^{-44} -2 q^{-46} - q^{-48} +3 q^{-50} - q^{-52} -2 q^{-54} +2 q^{-56} - q^{-60} + q^{-62} }
1,0,0
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^{12}-2 q^{10}+3 q^8-3 q^6+q^4+3 q^2-6+9 q^{-2} -12 q^{-4} +3 q^{-6} -6 q^{-8} -7 q^{-10} +3 q^{-12} -6 q^{-14} +10 q^{-16} - q^{-18} +21 q^{-20} - q^{-22} +26 q^{-24} +2 q^{-26} +11 q^{-28} +14 q^{-30} -16 q^{-32} +17 q^{-34} -23 q^{-36} +7 q^{-38} -20 q^{-40} -10 q^{-44} -10 q^{-46} +7 q^{-48} -19 q^{-50} +17 q^{-52} -12 q^{-54} +9 q^{-56} +3 q^{-58} -2 q^{-60} +6 q^{-62} -2 q^{-64} +2 q^{-66} -5 q^{-68} +6 q^{-70} -8 q^{-72} +4 q^{-74} +2 q^{-76} -7 q^{-78} +11 q^{-80} -7 q^{-82} +2 q^{-84} +4 q^{-86} -8 q^{-88} +6 q^{-90} -3 q^{-92} - q^{-94} +3 q^{-96} -2 q^{-98} + q^{-100} }

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^4- q^{-4} -3 q^{-6} -2 q^{-8} - q^{-10} - q^{-12} + q^{-16} +4 q^{-18} +3 q^{-20} +4 q^{-22} +4 q^{-24} +7 q^{-26} +6 q^{-28} +6 q^{-30} +3 q^{-32} +4 q^{-34} + q^{-36} -4 q^{-38} -4 q^{-40} -4 q^{-42} -6 q^{-44} -5 q^{-46} - q^{-48} -3 q^{-50} -2 q^{-52} + q^{-54} + q^{-56} -2 q^{-58} - q^{-60} +2 q^{-62} -2 q^{-66} + q^{-68} +2 q^{-70} + q^{-76} }
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 -1- q^{-4} + q^{-10} +2 q^{-12} + q^{-14} +3 q^{-16} + q^{-18} +3 q^{-20} + q^{-22} +2 q^{-24} - q^{-30} -2 q^{-32} - q^{-34} -2 q^{-36} - q^{-40} }

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^6+q^4-2 q^2+2-3 q^{-2} +4 q^{-4} -4 q^{-6} +4 q^{-8} -2 q^{-10} +3 q^{-12} + q^{-14} +4 q^{-18} -3 q^{-20} +6 q^{-22} -6 q^{-24} +7 q^{-26} -6 q^{-28} +5 q^{-30} -5 q^{-32} +3 q^{-34} -3 q^{-36} -2 q^{-42} +2 q^{-44} -2 q^{-46} +3 q^{-48} -3 q^{-50} +3 q^{-52} -2 q^{-54} +2 q^{-56} -2 q^{-58} + q^{-60} - q^{-62} }
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^{12}-q^8-q^6+q^4+q^2-2-3 q^{-2} +3 q^{-6} -3 q^{-10} - q^{-12} +4 q^{-14} +4 q^{-16} + q^{-18} -3 q^{-20} + q^{-22} +4 q^{-24} +4 q^{-26} - q^{-28} -2 q^{-30} +3 q^{-34} + q^{-36} - q^{-38} +2 q^{-42} -2 q^{-46} - q^{-48} + q^{-50} + q^{-52} -2 q^{-54} -3 q^{-56} - q^{-58} +2 q^{-60} -2 q^{-64} -2 q^{-66} + q^{-68} +2 q^{-70} -2 q^{-74} -2 q^{-76} + q^{-78} +3 q^{-80} + q^{-82} -2 q^{-84} -2 q^{-86} +2 q^{-90} + q^{-92} - q^{-94} - q^{-96} + q^{-100} }

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^6-q^4+q^2-2+2 q^{-2} -4 q^{-4} +2 q^{-6} -4 q^{-8} +3 q^{-10} -3 q^{-12} +2 q^{-14} - q^{-16} +3 q^{-18} +2 q^{-20} + q^{-22} +5 q^{-24} +2 q^{-26} +8 q^{-28} +8 q^{-32} -3 q^{-34} +6 q^{-36} -6 q^{-38} +2 q^{-40} -7 q^{-42} -6 q^{-46} -3 q^{-50} - q^{-56} + q^{-58} - q^{-60} +2 q^{-62} -2 q^{-64} + q^{-66} -2 q^{-68} +3 q^{-70} -2 q^{-72} + q^{-74} -2 q^{-76} +2 q^{-78} - q^{-80} + q^{-82} - q^{-84} + q^{-86} }

G2 Invariants.

Weight Invariant
1,0

.

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 5"];
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^4-3 t^3+5 t^2-5 t+5-5 t^{-1} +5 t^{-2} -3 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+5 z^6+7 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]= { 33, 4 }
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^9+2 q^8-3 q^7+4 q^6-5 q^5+5 q^4-4 q^3+4 q^2-2 q+2- q^{-1} }
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^{-4} -z^6 a^{-2} +7 z^6 a^{-4} -z^6 a^{-6} -5 z^4 a^{-2} +17 z^4 a^{-4} -5 z^4 a^{-6} -6 z^2 a^{-2} +17 z^2 a^{-4} -7 z^2 a^{-6} - a^{-2} +5 a^{-4} -3 a^{-6} }
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} +4 z^8 a^{-4} +2 z^8 a^{-6} +z^7 a^{-1} -3 z^7 a^{-3} -2 z^7 a^{-5} +2 z^7 a^{-7} -11 z^6 a^{-2} -20 z^6 a^{-4} -7 z^6 a^{-6} +2 z^6 a^{-8} -5 z^5 a^{-1} -2 z^5 a^{-3} -3 z^5 a^{-5} -4 z^5 a^{-7} +2 z^5 a^{-9} +18 z^4 a^{-2} +32 z^4 a^{-4} +10 z^4 a^{-6} -2 z^4 a^{-8} +2 z^4 a^{-10} +6 z^3 a^{-1} +7 z^3 a^{-3} +6 z^3 a^{-5} +3 z^3 a^{-7} -z^3 a^{-9} +z^3 a^{-11} -10 z^2 a^{-2} -22 z^2 a^{-4} -9 z^2 a^{-6} +z^2 a^{-8} -2 z^2 a^{-10} -z a^{-1} -2 z a^{-3} -3 z a^{-5} -z a^{-7} -z a^{-11} + a^{-2} +5 a^{-4} +3 a^{-6} }
Retrieved from "https://katlas.org/index.php?title=10_5&oldid=4510"