local w, a, b, c, result; w := E(3); a := E(15)^2+E(15)^8; b := E(15)^7+E(15)^13; # ComplexConjugate(a); c := E(5)+E(5)^4; result := rec(); result.comment := "6A6 as 12 x 12 matrices over the ring of \ integers of Q(z15^2+z15^8)\n\ "; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ ]; result.centralizeralgebra := [ ]; result.generators := [ [[0,-1,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0], [0,w^2,w,-w,0,0,0,0,0,0,0,0], [w,w^2,-1,-w,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0], [0,0,0,0,0,0,0,0,0,-w^2,-w,w], [0,0,0,0,0,0,0,0,-w,-w^2,1,w], [0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0], [0,0,0,0,0,-w^2,-w,w,0,0,0,0], [0,0,0,0,-w,-w^2,1,w,0,0,0,0]] , [[0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,1,w-w^2,-w,0,0,0,0,0], [0,0,0,0,-w^2,w,1,w,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,0], [-1,-w+w^2,w,0,0,0,0,0,0,0,0,0], [w^2,-w,-1,-w,0,0,0,0,0,0,0,0], [0,0,-b,0,0,0,-a,0,0,0,1,0], [0,0,0,-b,0,0,0,-a,0,0,0,1], [-b,2*a+b,c,0,-a,-a-2*b,b,0,1,w-w^2,-w,0], [a,-c,-b,-c,c,-b,-a,-b,-w^2,w,1,w]]]; return result;