Completions

[fieker]

decide on an interface to completions (padic, qadic, Avi, SeriesElem, Hamburger-Noether, ...)

• setprecision <-> set_precision (inplace and not) (for elements)
• lift, rational_reconstruct
• map_coeffs (for series)
• ResidueField (with cache parameter)
• precision handling for the ring, possibly following BigFloat
• induced precision handling for polynomials/ matrices over those rings (for lifting algorithms)
• common interface to roots of polynomials, factoring, gcd, resultant, ... (starting with the easy cases)
• stable linear algebra
• complete Euclidean interface
• padic/ qadic:
  • prime(ring, expo)
  • caching of Frobenius
  • Iwasawa log?

BIts and pieces already exists (PolyFactor for qadic, GaloisGrp (Oscar), MPolyFactor for Series, and in other places)

[fieker]

Constructor of SeriesElem: also support kw arguments:

• R([1,2,3, 4], 3, 5, 2) could be
• R([1,2,3, 4], length = 3, precision = 5, valuation = 2) This might be more readable.

Also

• add nmod_abs_series
• gpf_*_series
• think about REMOVING nmod_*_series (or make sure that they can handle non-primes)
• possibly the same to fmpz_mod stuff