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Old 2020-04-13, 13:54   #4
Nick
 
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Dec 2012
The Netherlands

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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 2020-04-13 at 20:19 Reason: Corrected typo
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