Re: the minimal polynomial over the composite field

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Aug 14, 2019 at 02:54:55PM +0900, macsyma wrote:
> Dear All,
> 
> As I mentioned in
> https://pari.math.u-bordeaux.fr/archives/pari-users-1908/msg00014.html ,
> I have the following (sub)goal:
> 
> "For a given irreducible g in Q[x], to find any one factor
>  (with the minimum positive degree) of g over the algebraic number field K
>  defined by polcyclo(p_1),...,polcyclo(p_m) where P={p_1,...,p_m}
>  is all of the odd prime factors of poldegree(g), in other words,
>  to find the minimal polynomial over K of an algebraic number defined by g."

Could you give more background about why you would like to compute that ?
In particular, are your polynomials g random ?
(in your examples they ave very specific shapes which allow to do the
computation nearly by hand).

Apparently your code factor first over Q(zeta_p+(zeta_p)^-1) and after
over Q(zeta_p). Does this give a measurable improvement ? If yes why
not try all the subfields from the smallest to the largest in turn ?

Cheers,
Bill.