
theorem
Discriminant X^2+X+1 = -3
proof
A1: (1+1) '*' 1.F_Rat
         = (1 '*' 1.F_Rat) + (1 '*' 1.F_Rat) by RING_3:62
        .= (1 '*' 1.F_Rat) + 1.F_Rat by RING_3:60
        .= 1.F_Rat + 1.F_Rat by RING_3:60
        .= 2 by GAUSSINT:13;
A2: (2+2) '*' 1.F_Rat
         = (2 '*' 1.F_Rat) + (2 '*' 1.F_Rat) by RING_3:62
        .= 4 by A1;
thus Discriminant X^2+X+1
         = (1.F_Rat)^2 - 4 '*' (1.F_Rat) by FIELD_9:def 10
        .= -3 by A2,GAUSSINT:13;
end;
