Is there a way in Pari to create the number field generated by elements in a fixed number field?
More precisely, suppose p in Q[x] is irreducible, and that q_1,...,q_n are polynomials in Q[x].
One can then create the elements a_i=Mod(q_i(x),p) in the number field defined by p.
I would like a command that takes p, and the q_i's as input and outputs a polynomial q generating the number field Q(a_1,...,a_n), as well as expressions of the a_i's in terms of q.
Surely, someone must have written a command that does that.
If someone could provide a script, or some hints for how to obtain this, I would really appreciate it.
Thanks a lot,