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[Axiom-developer] [PrimeField] (new)

From: Bill Page
Subject: [Axiom-developer] [PrimeField] (new)
Date: Wed, 12 Jan 2005 16:59:39 -0600

$GF(p)$ is called the prime field of order $p$, and is the field of residue 
classes modulo $p$, where the $p$ elements are denoted 0, 1, ..., . $a = b$ in 
$GF(p)$ means the same as $a \equiv b\ ({\bf mod}\  p)$. Note, however, that 
$2\times 2 \equiv 0\ ({\bf mod}\ 4)$ in the ring of residues modulo 4, so 2 has 
no reciprocal, and the ring of residues modulo 4 is distinct from the finite 
field with four elements. Finite fields are therefore denoted $GF(p^n)$, 
instead of $GF(k)$, where $k=p^n$, for clarity.

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