Why sage would give me polynomial representation of GF(8), but not GF(7)?
sage: G = GF(8, 'x')
sage: G.list()
[0, x, x^2, x + 1, x^2 + x, x^2 + x + 1, x^2 + 1, 1]
sage: G = GF(7, 'x')
sage: G.list()
[0, 1, 2, 3, 4, 5, 6]
Maybe there's no such thing as polynomial represenation of GF(7)?
If $p$ is a prime, then GF(p^n,'x') is obtained by computing $F_p[x] / (f(x))$ where $f$ is a monic, irreducible polynomial of degree $n$ in $F_p[x]$. For $n=1$, you just get $F_p[x] / (x) \cong F_p$.
So, for any prime $p$, GF(p,'x') is [0,1,2,...,p-1].
Asked: 2012-06-12 10:38:30 +0100
Seen: 618 times
Last updated: Jun 12 '12
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