Development roadmap for Nemo

[wbhart]

The following is a list of modules and other major components that remain to be implemented for Nemo.

GF(p)

• [X] GF(p) using nmod
• [ ] GF(p) using fmpz_mod

Relative power series

• [ ] arb_rel_series
• [ ] acb_rel_series

Laurent series

• [ ] fmpq_laurent_series
• [ ] nmod_laurent_series
• [ ] fmpz_mod_laurent_series
• [ ] fq_laurent_series
• [ ] fq_nmod_laurent_series
• [ ] arb_laurent_series
• [ ] acb_laurent_series

Puiseux series

• [ ] fmpq_puiseux_series
• [ ] nmod_puiseux_series
• [ ] fmpz_mod_puiseux_series
• [ ] fq_puiseux_series
• [ ] fq_nmod_puiseux_series
• [ ] arb_puiseux_series
• [ ] acb_puiseux_series

Absolute power series

• [ ] arb_abs_series
• [ ] acb_abs_series
• [ ] nmod_abs_series

Univariate polynomials

• [ ] O(d^2) Resultant over Z/nZ
• [ ] O(d^2) Reduced resultant over Z/nZ
• [ ] Polynomial time (??) Resx over Z/nZ (open problem)

Multivariate polynomials

• [ ] fmpz_mpoly
• [X] fmpq_mpoly
• [ ] nmod_mpoly

Number field arithmetic

• [ ] nf_elem_poly
• [ ] nf_elem_mat

Integer factorisation

• [ ] Smooth factoring
• [ ] Best of breed factoring
• [ ] Primality testing with certificate

Polynomial factorisation

• [ ] Pruned Zassenhaus over ZZ
• [ ] Multivariate factorisation over ZZ
• [ ] Multivariate factorisation over Z/pZ
• [ ] Univariate factorisation over number field
• [ ] Univariate irreducibility testing

Polynomial GCD

• [ ] Sparse GCD
• [ ] fmpz_mpoly_gcd
• [ ] nmod_mpoly_gcd
• [X] fmpq_mpoly_gcd

Miscellaneous

• [ ] Use Conda for binaries
• [ ] Citations module
• [ ] Julia serialisation
• [ ] Flint integration with Julia GC (nomangle fmpz pointers)
• [ ] Flint exception handling
• [ ] Handle impossible inverses over Z/nZ in Flint (CRT)

Performance issues

• [ ] Charpoly over Z with dim > 200
• [ ] O(n^3) minpoly (open problem)
• [ ] Determinant over Z
• [ ] Inverse of matrix over Z (with denominator)
• [ ] Determinant over Z/nZ
• [ ] Rank over F_p[x]
• [ ] Nullspace over F_p[x]