local w, result; w := E(3); result := rec(); result.comment := "U42 as 45 x 45 matrices\n\ "; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ ]; result.centralizeralgebra := [ ]; result.generators := [ [[w+3*w^2,2,-5*w,-w+2*w^2,w,-w-2*w^2,4*w-2*w^2,2*w-w^2,w+4*w^2,2*w+3*w^2,2*w-2*w^2,-w+w^2,-w^2,-w+3*w^2,w+3*w^2,-6*w-3*w^2,-3*w-w^2,3*w^2,1,-2*w-4*w^2,-w-3*w^2,w-w^2,w+3*w^2,2*w^2,-w,2*w-w^2,-w^2,-w-3*w^2,w-w^2,2*w^2, w,0,2*w^2,-3*w-2*w^2,2,-2*w-3*w^2,6*w+4*w^2,3*w^2,1,2,3*w+2*w^2,-2,-2,0,-2*w], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,1,-2*w,0,w,-1,w,-w,w^2,0,w^2,w^2,1,0,-w^2,1,-w,-w^2,-w^2,0,0,-w,0,0,-1,1,w,-1,-w, 0,0,0,-w^2,0,w,w^2,-w,1,0,w^2,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [-w,-w^2,-3*w-2*w^2,-2*w-w^2,w^2,-w^2,3*w+2*w^2,2*w+w^2,-2*w,w^2,2*w+w^2,-w,w,-2*w-w^2,-w+w^2,-w-3*w^2,1,-2*w,w,w-w^2,w-w^2,w,-w+w^2,-w,1,-1,0,w-w^2,-1,-w, -1,0,-w,-w-2*w^2,-w^2,w-w^2,w+3*w^2,-w,-w^2,-w^2,w+2*w^2,w^2,w^2,0,1], [-w,-w^2,-3*w-2*w^2,-w,w^2,-w^2,3*w+2*w^2,2*w+w^2,-2*w,w^2,2*w+w^2,0,w,-2*w-w^2,-w+w^2,-w-3*w^2,1,-w,0,w-w^2,w-w^2,-1,-w+w^2,-w,1,-1,0,w-w^2,w,-w, -1,0,-w,-w-2*w^2,-w^2,w-w^2,w+3*w^2,-w,0,-w^2,w+2*w^2,w^2,w^2,0,1], [w,w^2,2*w+w^2,-1,1,w^2,-2*w-w^2,-2*w-w^2,w-w^2,-w^2,-2*w,-1,w^2,2*w,w-w^2,2*w+3*w^2,-1,w,-w,-w+w^2,w^2,-w,-w^2,w,-1,1,-w,w^2,0,w, -w,0,w,-1,w^2,w^2,-2*w-3*w^2,w,-w,w^2,1,-w^2,-w^2,0,-1], [0,0,2*w^2,-1,0,1,w-w^2,-w^2,-1,w,1,0,-w^2,w^2,-1,-w,w^2,-1,0,1,1,0,-1,0,-w,-w^2,w^2,1,0,-1, w,0,0,-w,0,1,2*w,-1,0,1,w,0,0,0,0], [w-w^2,w^2,3*w+2*w^2,-1,1,w^2,-3*w-2*w^2,-2*w-w^2,w-w^2,-w^2,-3*w-w^2,-1,w^2,2*w,w-w^2,2*w+3*w^2,-1,2*w,-w,-w+w^2,-w+w^2,-w,-w^2,w,-1,1,-w,-w+w^2,0,w, 1,0,w,-1,w^2,2*w^2,-2*w-4*w^2,w,-w,w^2,-w-2*w^2,-w^2,-w^2,0,-1], [w^2,0,2,-2*w-w^2,-w^2,0,-1,-1,w^2,w^2,w,-w,w^2,0,-w,1,1,-w,-w^2,-w^2,w,-w^2,-w,w^2,-w^2,-1,-w^2,w,0,-w, w^2,0,0,-w^2,1,0,w+2*w^2,-w,-w^2,0,w^2,-1,0,0,0], [0,0,-w+2*w^2,3*w^2,w^2,-w-2*w^2,w-w^2,-2*w^2,w^2,-1,w,-1,w,-2*w,-1,2,-w,w+2*w^2,0,-2*w-w^2,1,0,w+2*w^2,0,-w,w,-w,-w-2*w^2,2*w,0, w,1,w^2,-2*w-w^2,w,-2*w^2,2*w+w^2,w^2,-w,-w^2,2*w+w^2,0,0,0,1], [0,0,2,-w,-w^2,w,-1,-1,w^2,w^2,0,0,-1,0,-w,0,1,-w,1,-w^2,w,0,-2*w-w^2,w^2,-w^2,w,1,w,0,w^2, w^2,-1,0,-w^2,-w,-1,w+2*w^2,-w+w^2,1,0,-w,0,0,1,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-w+w^2,-w^2,-4*w-3*w^2,-3*w-w^2,-1,w-w^2,4*w+3*w^2,3*w+w^2,-2*w+w^2,2*w^2,3*w+w^2,-w,w,-3*w-w^2,-w+w^2,-2*w-4*w^2,-w-2*w^2,-3*w,-w^2,w-2*w^2,w-w^2,w,-w+w^2,-w,1,-2,-w^2,2*w-w^2,-1,-2*w, -1,0,-w,-w-2*w^2,-w^2,w-w^2,2*w+5*w^2,-2*w,-w^2,-w^2,w+2*w^2,w^2,w^2,-w^2,1]]]; return result;