V1.02-1 (3 March 1995)

Recent Changes and Improvements

Totally New Categories

Power series and Laurent series (free and fixed precision).

Abelian groups.

Free-precision real and complex fields (from Pari system).

Valuation rings.

Rings and Fields

Ideals of most "interesting" rings.

Many ring predicates e.g. IsIntegralDomain.

Predicates on elements e.g. IsNilpotent.

Polynomial Rings

Improved factorization over Z and Q (using ideas from the recent paper "Improved Techniques in Univariate Polynomial Factorization" by G. Collins and M. Encarnacion).

Efficient GCD of univariate polynomials over Algebraic Number Fields using modular algorithm.

Factorization of univariate polynomials over Algebraic Number Fields.

General resultant algorithm.

Matrix Rings

Left/right/two-sided ideals, quotients, minimal/maximal ideals, radical, etc.

Quadratic Fields

Added features.

Improved functionality and bug fixes.

Finite Fields

Discrete logarithm (Pohlig-Hellman) for moderate-sized fields.

Modules

Submodule lattice.

General Hom and Endo algorithm for reducible modules.

Decomposability testing; Indecomposable summands.

Matrices

New efficient Hermite algorithms from G. Havas and B. Majewski.

Hermite form of a matrix with transformation matrix close to optimal in that its entries are all minimal using LLL based ideas.