Recall: pari-2.6.2 (testing, beta) will be out "real soon now", and is a
release-candidate for 2.7-stable.
New mathematical features for PARI-2.8 (testing) -> PARI-2.9 (stable)
* Elliptic curves
- over number fields
- descent
- include ratpoint ?
- modular equation (Hamish)
- isogeny matrix
- modular symbols, merge the kb-modsym2 branch
* Algebraic number theory
- dynamic nf (confer 'ell'): add new components dynamically as they are
computed (integer basis, class group/units...)
- compact S-units and fundamental units.
- rewrite bnfsunit to compute directly S-units without reducing to
fundamental units (which may be *much* larger)
- cyclotomic units / subfields to help bnfinit
- get rid of bnrinit(,,1): *no* function should need explicit expanded
generators, implicit descriptions in terms of linear algebra should be
enough.
- rnfkummer for composite degrees
- fix rnfkummer (fix and merge kb-rnfkummer)
- bnrisgalois
- polsturm -> Uspensky (merge loic-Uspensky)
- abstract / generalize ad hoc abelian groups constructions (short exact
sequences)
- central simple algebras (Aurel)
- Fieker-Klueners polgalois algorithm, GAP module using PARI ?
* L-functions (Pascal)
- Dirichlet character
- Hecke character
- L(s,\chi), at least for deg <=2
- Artin L-functions
* Multiprecision:
- merge the new-t_REAL branch
- go through transcendental functions and include rigorous / faster algorithms
- hooks to optionally link with mpfr / mpc higher lever routines