[GAP Forum] representation of Finite Field's element

MCKAY john mckay at encs.concordia.ca
Tue May 26 07:37:20 BST 2009

I find the Zech logarithm best for compying in finite fields.

Clement Lam & I have an algorithm in Collected Algorithms of
ACM "Arithmetic over a Finite Field"=Algorithm 469 [1973]..
Conway & Guy have a paper in a Blaricum conf proc about the i
same date (1970's edited by Herz).

For primitive a we have a^Z(k) = 1+a^k (k in {-inf,0,1,...q-2}).

Whence easy multiplication and addition of powers of a.
(a^r+a^s  (r <=s) = a^r(1+a^(s-r)).

On Tue, 26 May 2009, xiaolei zhang wrote:

> hello.
> GAP us a primitive element to generate a finite field, this is good for
> computation. But I want to use gap in teaching, so I need some other
> representation of element.
> say, F2={0,1}¡¤ F2[x]/(x^2+x+1) ={0, 1, 1+x, x}
> In GAP, can I use the root of x^2+x+1 to represent the element of GF(4)?
> thanks
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