Mochizuki 3-cocycle invariants for Alexander Quandles 3-cocycle formula f(x,y,z)=(x-y)^3^0 *(y-z)^3^1 *z^0 Alexander Quandle Z_3[t^1,t^-1]/(t^2+1) 4_1 [1, -2, 1, -2] Gcd(t^2+1,t^2-3*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 5_2 [1, 1, 1, 2, -1, 2] Gcd(t^2+1,2*t^2-3*t+2) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 6_3 [1, 1, -2, 1, -2, -2] Gcd(t^2+1,t^4-3*t^3+5*t^2-3*t+1) mod 3 =t^2+1 729 8_2 [1, 1, 1, 1, 1, -2, 1, -2] Gcd(t^2+1,t^6-3*t^5+3*t^4-3*t^3+3*t^2-3*t+1) mod 3 =t^2+1 729 8_3 [1, 1, 2, -1, -3, 2, -3, -4, 3, -4] Gcd(t^2+1,4*t^2-9*t+4) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 8_6 [1, 1, 1, 1, 2, -1, -3, 2, -3] Gcd(t^2+1,2*t^4-6*t^3+7*t^2-6*t+2) mod 3 =t^2+1 729 8_17 [1, 1, -2, 1, -2, 1, -2, -2] Gcd(t^2+1,t^6-4*t^5+8*t^4-11*t^3+8*t^2-4*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 8_18 [1, -2, 1, -2, 1, -2, 1, -2] Gcd(t^2+1,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 8_19 [1, 1, 1, 2, 1, 1, 1, 2] Gcd(t^2+1,t^6-t^5+t^3-t+1) mod 3 =t^2+1 729 8_21 [1, 1, 1, 2, -1, -1, 2, 2] Gcd(t^2+1,t^4-4*t^3+5*t^2-4*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_3 [1, 1, 1, 1, 1, 1, 1, 2, -1, 2] Gcd(t^2+1,2*t^6-3*t^5+3*t^4-3*t^3+3*t^2-3*t+2) mod 3 =t^2+1 729 9_6 [1, 1, 1, 1, 1, 1, 2, -1, 2, 2] Gcd(t^2+1,2*t^6-4*t^5+5*t^4-5*t^3+5*t^2-4*t+2) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_7 [1, 1, 1, 1, 2, -1, 2, 3, -2, 3, 3] Gcd(t^2+1,3*t^4-7*t^3+9*t^2-7*t+3) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_11 [1, 1, 1, 1, -2, 1, 3, -2, 3] Gcd(t^2+1,t^6-5*t^5+7*t^4-7*t^3+7*t^2-5*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_12 [1, 1, -2, 1, 3, -2, 3, 4, -3, 4] Gcd(t^2+1,2*t^4-9*t^3+13*t^2-9*t+2) mod 3 =t^2+1 729 9_13 [1, 1, 1, 1, 2, -1, 2, 2, 3, -2, 3] Gcd(t^2+1,4*t^4-9*t^3+11*t^2-9*t+4) mod 3 =t^2+1 729 9_24 [1, 1, -2, 1, 3, -2, -2, -2, 3] Gcd(t^2+1,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_26 [1, 1, 1, -2, 1, -2, 3, -2, 3] Gcd(t^2+1,t^6-5*t^5+11*t^4-13*t^3+11*t^2-5*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_37 [1, 1, -2, 1, 3, -2, -1, -4, 3, -2, 3, -4] Gcd(t^2+1,2*t^4-11*t^3+19*t^2-11*t+2) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_38 [1, 1, 2, 2, -3, 2, -1, 2, 3, 3, 2] Gcd(t^2+1,5*t^4-14*t^3+19*t^2-14*t+5) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_39 [1, 1, 2, -1, -3, -2, 1, 4, 3, -2, 3, 4] Gcd(t^2+1,3*t^4-14*t^3+21*t^2-14*t+3) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2) 9_40 [1, -2, 1, 3, -2, 1, 3, -2, 3] Gcd(t^2+1,t^6-7*t^5+18*t^4-23*t^3+18*t^2-7*t+1) mod 3 =t^2+1 2673+1944*u^(t+2)+1944*u^(2*t+1) 9_47 [1, -2, 1, -2, -3, -2, 1, -2, -3] Gcd(t^2+1,t^6-4*t^5+6*t^4-5*t^3+6*t^2-4*t+1) mod 3 =t^2+1 729 9_48 [1, 1, 2, -1, 2, 1, -3, 2, -1, 2, -3] Gcd(t^2+1,t^4-7*t^3+11*t^2-7*t+1) mod 3 =t^2+1 81+324*u^(2*t+1)+324*u^(t+2)