Hey all,
I have two series of patches I've been working on and need some help
reviewing them.

The first implements coercion within lattices of finite fields.  So you can
now do the following:

sage: k = GF(9)
sage: l = GF(27)
sage: x = k.gen() + l.gen(); x
z6^5 + 2*z6^4 + 2*z6^3 + z6^2 + 2*z6 + 1
sage: x.parent()
Finite Field in z6 of size 3^6
sage: K.<a> = GF(2^1000)
sage: K.subfields()
<big list of subfields of K with embeddings into K>

Along the way I've moved the finite rings into their own folder
(sage.rings.finite_rings), moved finite fields and orders of number fields
to the new coercion system, sped up nth roots in finite fields and
IntegerMods and more.  This is the series of tickets
#8218 -> #8332 -> #7880 -> #7883 -> #8333 -> #8334 -> #8335,
and they all need review.

The second is a collection of changes to p-adic polynomials at ticket
#6084.  It's not quite ready for review, but it's been languishing for the
summer and I could use some help looking at it.  Kiran has volunteered, but
there's a lot of code there and he'd like some assistance.  The idea behind
the changes is to try to split off the precision and coefficient data for
p-adic polynomials and model them separately.  This allows one to work with
different styles of precision (newton polygons, list of absolute precisions,
flat precisions) attached to different coefficient implementations (FLINT
backend, NTL_ZZ_pX, NTL_ZZ_pEX) using good multiplication algorithms.  If
you're interested in helping, comment on the ticket or e-mail me.

Finally, I'd like to plug #7716, which improves the sage-coverage script and
currently needs review.
David

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