Release Notes V1.02-1 (3 March 1995)

Magma 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.

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.