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+2) 3_1 [1, 1, 1] Gcd(t^2+2,t^2-t+1) mod 3 =t+1 243 6_1 [1, 1, 2, -1, -3, 2, -3] Gcd(t^2+2,2*t^2-5*t+2) mod 3 =t+1 243 7_4 [1, 1, 2, -1, 2, 2, 3, -2, 3] Gcd(t^2+2,4*t^2-7*t+4) mod 3 =t+1 243 7_7 [1, -2, 1, -2, 3, -2, 3] Gcd(t^2+2,t^4-5*t^3+9*t^2-5*t+1) mod 3 =t+1 243 8_5 [1, 1, 1, -2, 1, 1, 1, -2] Gcd(t^2+2,t^6-3*t^5+4*t^4-5*t^3+4*t^2-3*t+1) mod 3 =t+1 243 8_10 [1, 1, 1, -2, 1, 1, -2, -2] Gcd(t^2+2,t^6-3*t^5+6*t^4-7*t^3+6*t^2-3*t+1) mod 3 =t+1 243 8_11 [1, 1, 2, -1, 2, 2, -3, 2, -3] Gcd(t^2+2,2*t^4-7*t^3+9*t^2-7*t+2) mod 3 =t+1 243 8_15 [1, 1, -2, 1, 3, 2, 2, 2, 3] Gcd(t^2+2,3*t^4-8*t^3+11*t^2-8*t+3) mod 3 =t+1 243 8_18 [1, -2, 1, -2, 1, -2, 1, -2] Gcd(t^2+2,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 3 =t+1 729 8_19 [1, 1, 1, 2, 1, 1, 1, 2] Gcd(t^2+2,t^6-t^5+t^3-t+1) mod 3 =t+1 243 8_20 [1, 1, 1, -2, -1, -1, -1, -2] Gcd(t^2+2,t^4-2*t^3+3*t^2-2*t+1) mod 3 =t+1 243 8_21 [1, 1, 1, 2, -1, -1, 2, 2] Gcd(t^2+2,t^4-4*t^3+5*t^2-4*t+1) mod 3 =t+1 243 9_1 [1, 1, 1, 1, 1, 1, 1, 1, 1] Gcd(t^2+2,t^8-t^7+t^6-t^5+t^4-t^3+t^2-t+1) mod 3 =t+1 243 9_2 [1, 1, 1, 2, -1, 2, 3, -2, 3, 4, -3, 4] Gcd(t^2+2,4*t^2-7*t+4) mod 3 =t+1 243 9_4 [1, 1, 1, 1, 1, 2, -1, 2, 3, -2, 3] Gcd(t^2+2,3*t^4-5*t^3+5*t^2-5*t+3) mod 3 =t+1 243 9_6 [1, 1, 1, 1, 1, 1, 2, -1, 2, 2] Gcd(t^2+2,2*t^6-4*t^5+5*t^4-5*t^3+5*t^2-4*t+2) mod 3 =t+1 243 9_10 [1, 1, 2, -1, 2, 2, 2, 2, 3, -2, 3] Gcd(t^2+2,4*t^4-8*t^3+9*t^2-8*t+4) mod 3 =t+1 243 9_11 [1, 1, 1, 1, -2, 1, 3, -2, 3] Gcd(t^2+2,t^6-5*t^5+7*t^4-7*t^3+7*t^2-5*t+1) mod 3 =t+1 243 9_15 [1, 1, 1, 2, -1, -3, 2, 4, -3, 4] Gcd(t^2+2,2*t^4-10*t^3+15*t^2-10*t+2) mod 3 =t+1 243 9_16 [1, 1, 1, 1, 2, 2, -1, 2, 2, 2] Gcd(t^2+2,2*t^6-5*t^5+8*t^4-9*t^3+8*t^2-5*t+2) mod 3 =t+1 243 9_17 [1, -2, 1, -2, -2, -2, 3, -2, 3] Gcd(t^2+2,t^6-5*t^5+9*t^4-9*t^3+9*t^2-5*t+1) mod 3 =t+1 243 9_23 [1, 1, 1, 2, -1, 2, 2, 3, -2, 3, 3] Gcd(t^2+2,4*t^4-11*t^3+15*t^2-11*t+4) mod 3 =t+1 243 9_24 [1, 1, -2, 1, 3, -2, -2, -2, 3] Gcd(t^2+2,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 3 =t+1 243 9_28 [1, 1, -2, 1, 3, -2, -2, 3, 3] Gcd(t^2+2,t^6-5*t^5+12*t^4-15*t^3+12*t^2-5*t+1) mod 3 =t+1 243 9_29 [1, -2, -2, 3, -2, 1, -2, 3, -2] Gcd(t^2+2,t^6-5*t^5+12*t^4-15*t^3+12*t^2-5*t+1) mod 3 =t+1 243 9_34 [1, -2, 1, -2, 3, -2, 1, -2, 3] Gcd(t^2+2,t^6-6*t^5+16*t^4-23*t^3+16*t^2-6*t+1) mod 3 =t+1 243 9_35 [1, 1, 2, -1, 2, 2, 3, -2, -2, 4, -3, 2, 4, 3] Gcd(t^2+2,7*t^2-13*t+7) mod 3 =t+1 729 9_37 [1, 1, -2, 1, 3, -2, -1, -4, 3, -2, 3, -4] Gcd(t^2+2,2*t^4-11*t^3+19*t^2-11*t+2) mod 3 =t+1 729 9_38 [1, 1, 2, 2, -3, 2, -1, 2, 3, 3, 2] Gcd(t^2+2,5*t^4-14*t^3+19*t^2-14*t+5) mod 3 =t+1 243 9_40 [1, -2, 1, 3, -2, 1, 3, -2, 3] Gcd(t^2+2,t^6-7*t^5+18*t^4-23*t^3+18*t^2-7*t+1) mod 3 =t+1 243 9_46 [1, -2, 1, -2, 3, 2, -1, 2, 3] Gcd(t^2+2,2*t^2-5*t+2) mod 3 =t+1 729 9_47 [1, -2, 1, -2, -3, -2, 1, -2, -3] Gcd(t^2+2,t^6-4*t^5+6*t^4-5*t^3+6*t^2-4*t+1) mod 3 =t+1 729 9_48 [1, 1, 2, -1, 2, 1, -3, 2, -1, 2, -3] Gcd(t^2+2,t^4-7*t^3+11*t^2-7*t+1) mod 3 =t+1 729