showtime : true;
A : matrix( [x1,x2,x3,x4,x5,x6,x7,x8],
            [x2,x3,x4,x5,x6,x7,x8,x1],
            [x3,x4,x5,x6,x7,x8,x1,x2],
            [x4,x5,x6,x7,x8,x1,x2,x3],
            [x5,x6,x7,x8,x1,x2,x3,x4],
            [x6,x7,x8,x1,x2,x3,x4,x5],
            [x7,x8,x1,x2,x3,x4,x5,x6],
            [x8,x1,x2,x3,x4,x5,x6,x7] );
/* ratmx : true; */
D : determinant(A)$
D : ratexpand(D)$
nterms(D);
F : factor(D)$