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 Fp[x]/(f(x)) where f is a monic, irreducible polynomial of degree n in Fp[x]. For n=1, you just get Fp[x]/(x)≅Fp.
So, for any prime p, GF(p,'x') is [0,1,2,...,p-1].
Oh I see - so it's just because `n=1`. Thank You for Your answer.
Asked: 12 years ago
Seen: 755 times
Last updated: Jun 12 '12
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