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