The high level changes in detail are:
- ATLAS: Michael Abshoff and Burcin Erocal upgraded ATLAS to the 3.8.1 release. In addition tuning info for 32 bit Prescott CPUs as well as Powerbook G4s under Linux was added.
- zn_poly: David Harvey's zn_poly library is now a standard package for Sage. zn_poly is a new C library for polynomial arithmetic in (Z/nZ)[x] where 3≤n≤ULONG_MAX (i.e. any machine-word-sized modulus). The main benefit is speed. The library is used so far only to compute the zeta function for hyperelliptic curves.
- Small roots method for polynomials mod N (N composite): Martin Albrecht implemented Coppersmith's method for finding small roots of univariate polynomials modulo N where N is composite.
- Generic Multivariate Polynomial Arithmetic: Joel Mohler improved the efficiency of the generic multivariate polynomial arithmetic in Sage by roughly a factor of ten.
- k-Schur Functions and Non-symmetric Macdonald Polynomials: Mike Hansen: k-Schur functions s^(k)_\lambda are a relatively new family of symmetric functions which play a role in Z[h1,...,hk] as the Schur functions s_\lambda do in \Lambda. The k-Schur functions, amongst other things, provide a natural basis for the quantum cohomology of the Grassmannian. The k-Schur functions can be used like any other symmetric functions and are created with kSchurFunctions. Non-symmetric Macdonald polynomials in type A can now be accessed in Sage. The polynomials are computed from the main theorem in "A Combinatorial Formula for the Non-symmetric Macdonald Polynomials" by Haglun, Haiman, and Loehr.
- Marshall Hampton did upgrade gfan as well as the optional phcpack spkgs and their interfaces. He also increased doctest coverage to 100% for both interfaces.
- Improved capabilities for solving matrix equations: William Stein implemented code so that one can now solve matrix equations AX=B and XA=B whenever a solution exists. In particular, solving linear equations now works even if A is singular or nonsquare.
- Generators for congruence subgroups: Robert Miller implemented an algorithm for very quickly computing generators for congruence subgroups \Gamma_0(N), \Gamma_1(N), and \Gamma_H(N).
- Various other people fixed a number of bugs and did improve other bits of Sage.