Let's take your example of q=7. If
\[f_0\zeta^0+f_1\zeta^1+f_2\zeta^2+f_3\zeta^3+f_4\zeta^4+f_5\zeta^5=
g_0\zeta^0+g_1\zeta^1+g_2\zeta^2+g_3\zeta^3+g_4\zeta^4+g_5\zeta^5\]
where the \(f_i\) and \(g_i\) are polynomials with integer (or rational) coefficients
then \(f_0=g_0\), \(f_1=g_1\),...,\(f_6=g_6\).
So it's not a problem if the polynomial F has a constant term.
Replacing \(\zeta\) with \(\zeta^m\) permutes the coefficients of \(\zeta^1\) up to \(\zeta^6\) and leaves \(\zeta^0\) unaltered.
Last fiddled with by Nick on 20200413 at 20:19
Reason: Corrected typo
