Johannes Grabmeier wrote:
> I found a criterium for binomials over finite fields to be irreducible,
Criterion for all fields is given in S. Lang "Algebra", in Polish
edition this is Chaper 8, section 9, theorem 16 (this follows
section on Kummer theory). The criteion is easily specialized
to finite fields. As I wrote one gets from it criterion
for existence of irreducible binomials.
Another question is if we can _quickly_ find irreducible binomial?
Already in Z_p we are in trouble, as fraction of suitable elements
may be quite low. And if we want to use sequential search, then
we are on shaky ground. IIUC already for quadratic extension
ability to quicky find quadratic nonresidue depends on GRH (
generalized Riemman hypothesis).
--
Waldek Hebisch
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/fricas-devel/E1ia0OX-0005dQ-TC%40hera.math.uni.wroc.pl.
