Mochizuki 3-cocycle invariants for Alexander Quandles 3-cocycle formula f(x,y,z)=(x-y)^2^0 *(y-z)^2^1 *z^0 Alexander Quandle Z_2[t^1,t^-1]/(t^3+1) 3_1 [1, 1, 1] Gcd(t^3+1,t^2-t+1) mod 2 =t^2+t+1 64+192*u^(t^2+1) 4_1 [1, -2, 1, -2] Gcd(t^3+1,t^2-3*t+1) mod 2 =t^2+t+1 64+192*u^(t^2+1) 7_2 [1, 1, 1, 2, -1, 2, 3, -2, 3] Gcd(t^3+1,3*t^2-5*t+3) mod 2 =t^2+t+1 64+192*u^(t^2+1) 7_3 [1, 1, 1, 1, 1, 2, -1, 2] Gcd(t^3+1,2*t^4-3*t^3+3*t^2-3*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 8_1 [1, 1, 2, -1, 2, 3, -2, -4, 3, -4] Gcd(t^3+1,3*t^2-7*t+3) mod 2 =t^2+t+1 64+192*u^(t^2+1) 8_4 [1, 1, 1, -2, 1, -2, -3, 2, -3] Gcd(t^3+1,2*t^4-5*t^3+5*t^2-5*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 8_5 [1, 1, 1, -2, 1, 1, 1, -2] Gcd(t^3+1,t^6-3*t^5+4*t^4-5*t^3+4*t^2-3*t+1) mod 2 =t^2+t+1 256 8_10 [1, 1, 1, -2, 1, 1, -2, -2] Gcd(t^3+1,t^6-3*t^5+6*t^4-7*t^3+6*t^2-3*t+1) mod 2 =t^2+t+1 256 8_11 [1, 1, 2, -1, 2, 2, -3, 2, -3] Gcd(t^3+1,2*t^4-7*t^3+9*t^2-7*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 8_13 [1, 1, -2, 1, -2, -2, -3, 2, -3] Gcd(t^3+1,2*t^4-7*t^3+11*t^2-7*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 8_15 [1, 1, -2, 1, 3, 2, 2, 2, 3] Gcd(t^3+1,3*t^4-8*t^3+11*t^2-8*t+3) mod 2 =t^2+t+1 256 8_18 [1, -2, 1, -2, 1, -2, 1, -2] Gcd(t^3+1,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 2 =t^2+t+1 256+768*u^(t^2+1) 8_19 [1, 1, 1, 2, 1, 1, 1, 2] Gcd(t^3+1,t^6-t^5+t^3-t+1) mod 2 =t^2+t+1 256 8_20 [1, 1, 1, -2, -1, -1, -1, -2] Gcd(t^3+1,t^4-2*t^3+3*t^2-2*t+1) mod 2 =t^2+t+1 256 8_21 [1, 1, 1, 2, -1, -1, 2, 2] Gcd(t^3+1,t^4-4*t^3+5*t^2-4*t+1) mod 2 =t^2+t+1 256 9_1 [1, 1, 1, 1, 1, 1, 1, 1, 1] Gcd(t^3+1,t^8-t^7+t^6-t^5+t^4-t^3+t^2-t+1) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_6 [1, 1, 1, 1, 1, 1, 2, -1, 2, 2] Gcd(t^3+1,2*t^6-4*t^5+5*t^4-5*t^3+5*t^2-4*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_12 [1, 1, -2, 1, 3, -2, 3, 4, -3, 4] Gcd(t^3+1,2*t^4-9*t^3+13*t^2-9*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_13 [1, 1, 1, 1, 2, -1, 2, 2, 3, -2, 3] Gcd(t^3+1,4*t^4-9*t^3+11*t^2-9*t+4) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_14 [1, 1, 2, -1, -3, 2, -3, 4, -3, 4] Gcd(t^3+1,2*t^4-9*t^3+15*t^2-9*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_16 [1, 1, 1, 1, 2, 2, -1, 2, 2, 2] Gcd(t^3+1,2*t^6-5*t^5+8*t^4-9*t^3+8*t^2-5*t+2) mod 2 =t^2+t+1 256 9_21 [1, 1, 2, -1, 2, -3, 2, 4, -3, 4] Gcd(t^3+1,2*t^4-11*t^3+17*t^2-11*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_22 [1, -2, 1, -2, 3, -2, -2, -2, 3] Gcd(t^3+1,t^6-5*t^5+10*t^4-11*t^3+10*t^2-5*t+1) mod 2 =t^2+t+1 256 9_23 [1, 1, 1, 2, -1, 2, 2, 3, -2, 3, 3] Gcd(t^3+1,4*t^4-11*t^3+15*t^2-11*t+4) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_24 [1, 1, -2, 1, 3, -2, -2, -2, 3] Gcd(t^3+1,t^6-5*t^5+10*t^4-13*t^3+10*t^2-5*t+1) mod 2 =t^2+t+1 256 9_25 [1, 1, -2, 1, 3, 2, 2, -4, 3, -4] Gcd(t^3+1,3*t^4-12*t^3+17*t^2-12*t+3) mod 2 =t^2+t+1 256 9_28 [1, 1, -2, 1, 3, -2, -2, 3, 3] Gcd(t^3+1,t^6-5*t^5+12*t^4-15*t^3+12*t^2-5*t+1) mod 2 =t^2+t+1 256 9_29 [1, -2, -2, 3, -2, 1, -2, 3, -2] Gcd(t^3+1,t^6-5*t^5+12*t^4-15*t^3+12*t^2-5*t+1) mod 2 =t^2+t+1 256 9_30 [1, 1, -2, -2, 1, -2, 3, -2, 3] Gcd(t^3+1,t^6-5*t^5+12*t^4-17*t^3+12*t^2-5*t+1) mod 2 =t^2+t+1 256 9_35 [1, 1, 2, -1, 2, 2, 3, -2, -2, 4, -3, 2, 4, 3] Gcd(t^3+1,7*t^2-13*t+7) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_36 [1, 1, 1, -2, 1, 1, 3, -2, 3] Gcd(t^3+1,t^6-5*t^5+8*t^4-9*t^3+8*t^2-5*t+1) mod 2 =t^2+t+1 256 9_37 [1, 1, -2, 1, 3, -2, -1, -4, 3, -2, 3, -4] Gcd(t^3+1,2*t^4-11*t^3+19*t^2-11*t+2) mod 2 =t^2+t+1 64+192*u^(t^2+1) 9_38 [1, 1, 2, 2, -3, 2, -1, 2, 3, 3, 2] Gcd(t^3+1,5*t^4-14*t^3+19*t^2-14*t+5) mod 2 =t^2+t+1 256 9_39 [1, 1, 2, -1, -3, -2, 1, 4, 3, -2, 3, 4] Gcd(t^3+1,3*t^4-14*t^3+21*t^2-14*t+3) mod 2 =t^2+t+1 256 9_40 [1, -2, 1, 3, -2, 1, 3, -2, 3] Gcd(t^3+1,t^6-7*t^5+18*t^4-23*t^3+18*t^2-7*t+1) mod 2 =t^2+t+1 256+768*u^(t^2+1) 9_41 [1, 1, 2, -1, -3, -2, -2, 4, 3, -2, 3, 4] Gcd(t^3+1,3*t^4-12*t^3+19*t^2-12*t+3) mod 2 =t^2+t+1 256 9_42 [1, 1, 1, -2, -1, -1, 3, -2, 3] Gcd(t^3+1,t^4-2*t^3+t^2-2*t+1) mod 2 =t^2+t+1 256 9_43 [1, 1, 1, 2, 1, 1, -3, 2, -3] Gcd(t^3+1,t^6-3*t^5+2*t^4-t^3+2*t^2-3*t+1) mod 2 =t^2+t+1 256 9_44 [1, 1, 1, 2, -1, -1, -3, 2, -3] Gcd(t^3+1,t^4-4*t^3+7*t^2-4*t+1) mod 2 =t^2+t+1 256 9_45 [1, 1, 2, -1, 2, 1, 3, -2, 3] Gcd(t^3+1,t^4-6*t^3+9*t^2-6*t+1) mod 2 =t^2+t+1 256 9_49 [1, 1, 2, 1, 1, -3, 2, -1, 2, 3, 3] Gcd(t^3+1,3*t^4-6*t^3+7*t^2-6*t+3) mod 2 =t^2+t+1 256