Work list

[fredrik-johansson]

Big initial todo list.

Urgent (before 0.1 release):

• use field cache with hash table
• fix hash functions
• mctx persistent pointers (add indirection)
• improve qqbar_root_ui
• cache acb enclosures
• implement all ca_check_X methods
• complex parts
• string conversion, better printing
• some example programs

Important:

• continuous integration
• check build system
• stronger tests (check that some basic simplifications really work, not just giving UNKNOWN)
• clean up all structs and macros
• fix/unity field_init methods
• change ideal to ** to avoid copies
• recycle storage in make_field_element
• move nf_t to field object
• optimize field/extension insertion/lookup (avoid duplicate allocations, copies)
• rename ca_check_X methods?
• separate fast and slow check methods
• organize the code for inserting extra field elements -- what is the right place to do this?
• some more simplifications for major transcendental functions (exp, log, some trig functions)
• use factorisation in abs, sign, ...
• convert mixed algebraic number to single number field
• decent field pruning (remove unused elements, all powers of x^(1/n) divisible by n -> x (etc...)
• transfer between context objects
• functions to decompose ca_t -> mpoly_q + ext list (etc.)
• special values for pow
• separate in-field / inert powering
• optimize subtraction

Long-term:

• reference counting for extension numbers and fields (with recycle bins)
• more intelligent adaptive numerical evaluation
• more intelligent qqbar simplification
• algorithms for mixed algebraic/transcendental simplification
• optimized fmpz_mpoly_q composition and evaluation (fmpz_mpoly_q, arb, acb)
• simplifying number fields
• number field embeddings
• lots of optimizations for roots of unity and nth roots
• more transcendentals
• polynomials, matrices
• radical denesting (outside of qqbar, also for radicals involving transcendentals)
• add a simple expression parser (useful for test code)
• Gröbner bases
• good Gröbner basis code / plug in fast external GB engine
• user-defined extension numbers