TODO.md

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 nf_elem in NfOrd

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