Construct a "complex" finite field?

[Fabian Werner <werner@rbg.informatik.tu-darmstadt.de>]

Hi everybody.


Is it possible to define the following using pari?

((Z/2Z)[a] / a2 + a + 1) [x] / g(x)

where g(x) is an irreducible polynome of degree n.

I have a finite field Z/2Z
Now i want to extend it by some irreducible polynome of degree m (in this example, m was 2)
Now i obtain a finite field again.
Finally, i want to extend this field again by some g(x).

Is this possible? Ive tried Singular and some others, but i was only able to do one single extension of (Z/pZ).

By the way: is it possible to obtain an irreducible polynome of degree n using pari?

kind regards + THX in advance!!

Fabian Werner

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