The problem with having Axiom "automatically" perform a irreducibility
check is that the check could be time consuming. Suppose you have a
polynomial of high degree whose factorization takes, say, a couple of
minutes. With an automatic irreducibility test, AXIOM would factor the
polynomial every time you create the finite field, which is probably not
what you would want.
I didn't consider this aspect. You are right: it can be quite annoying
indeed.
If there is no way out from this, maybe it could be worth to stress in the
documentation this point and the fact tha the user _must_ take care of the
chosen polynomial.
Fabio
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