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TODO.md

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Todo list for rainy days

General

  • Provide (prototype) documentation in the following formats: REPL using @doc, html, as well as pdf
  • Copyright information (BSD 2-clause) in each file
  • Build a (user)sysimage to speed up starting time

Orders in number fields

  • implement Montes--Nart algorithm
  • composite Dedekind criterion
  • composite Round Two algorithm
  • implement information about containment (O_1 \sub O_2)
  • save prime factors of discriminant
  • princ_gen should be cached
  • Clean up uniformizer (p-uniformizer? strong uniformizer?)
  • Residue fields of degree one
  • Parent checks for (::Order)(::NumFieldElem).
  • Coercion of AbsSimpleNumFieldElem in AbsSimpleNumFieldOrder

Number fields

  • Overhaul the morphisms
  • Test functionality for non-monic defining polynomials
  • Torsion unit functionality for number fields
  • Better algorithm for normal closure
  • weak and strong approximation
  • absolute_field is inconsistent and needs keyword for simplify
  • Remove the type nf_elem_or_fac_elem
  • Clean up the clever princ_gen_special code
  • Implement Arakelov and/or divisor type
  • Finite places
  • Need is_maximal_order_known and isautomorphism_group_known
  • relative_extension
  • is_locally_power (at given primes or up to given bound)
  • Frobenius automorphism of a field at a prime ideal
  • Redo the automorphism_group properly.
  • coeff(z, i) and coefficients(z) "inconsistencies"

Renaming

  • DiagonalGroup and AbelianGroup to abelian_group.
  • princ_gen to principal_generator
  • nf to number_field
  • Group algebra renaming
  • Make has* and *_known consistent.

Misc

  • exp_map_unit_grp_mod
  • charpoly should have parent = keyword.
  • Squarefree factorization over number fields (?)
  • Make FF robust for the use of ZZRingElem.
  • next_prime(::ZZRingElem, ::Bool)
  • round(::Type{QQFieldElem}, ::ZZRingElem) is doing funky things. Also needs the RoundUp/RoundDown versions.
  • Parent checks for factored elements
  • Primitive element for all finite fields