I'm doing a lot of arithmetic in finite fields, using Julia and the Nemo package (https://nemocas.github.io/Nemo.jl/stable/finitefield/). The documentation says
@doc raw"""
gen(a::FqPolyRepField)
Return the generator of the finite field. Note that this is only guaranteed
to be a multiplicative generator if the finite field is generated by a
Conway polynomial automatically.
"""
For mathematical reasons, I need a multiplicative generator. Ergo, I need to know which fields are "generated by a Conway polynomial automatically." Nemo uses flint (https://flintlib.org/sphinx/fq.html?highlight=conway#c._fq_ctx_init_conway), whose documentation contains similar language, referring to a database of Conway polynomials. Now, flint has a function that detects if the field is in the database, but I dont' know how to call that function from Julia.
Does Nemo use a particular version of flint, or the latest version, and how could I figure that out? A Conway polynomial exists for each prime power $p^e$, how can I learn (preferably within Julia) which ones are in the flint database that is summoned by Nemo?
