Release Notes V1.11-1

Magma V1.11-1 (20/12/95)

Recent Changes and Improvements

Algebraic Number Theory

• Installation of the new KANT V5 Algebraic Number Theory package

Coding Theory

• Weight Distribution speeded up
• Weight Enumerator
• Complete Weight Enumerator

Finite Fields

• Multiplicative and additive groups

Integer Ring

• Cunningham Factorization database
• A.K. Lenstra's Quadratic Sieve Factorization algorithm

Matrix Groups

• Element centralizer, intersection, subspace stabilizer backtracks
• Conjugacy classes, Class Map
• Character Table
• Stabilizer, Core
• BSGS access functions
• Generator image homomorphisms, Inverse word map, Word Group
• Upper Central series, Composition Factors
• Simplicity test
• GModule construction from elementary abelian sections
• Frattini Subgroup, SylowSubgroup, PC Group, SolvableQuotient
• Orbits with limit, Orbit actions using ImageKernel
• Assertable Attributes -- Classes, Base, Order, FactoredOrder, IsVerified

PC Groups

• Composition Series with natural representation

Permutation Groups

• Socle, Chief Series
• Sylow Subgroup, EARNS improvements
• Solvable quotient

Orbits with limit, Orbit actions using ImageKernel

Modules

• Modules over multivariate polynomial rings
• Syzygy modules

P-adic Fields

• Factorization of univariate polynomials over padic fields

Multivariate Polynomial Rings

• Completely new multivariate polynomial system with distributive form and different term orders
• The GCD-HEU GCD algorithm
• The EEZ sparse GCD algorithm
• The EEZ Factorization algorithm
• Ideals and Groebner bases
• The Groebner Walk algorithm
• Varieties
• Elimination Ideals
• Relation Ideals
• Quotient Rings
• Symmetric Polynomials

Quadratic Fields

• QuadraticOrder capability
• NormEquation substantially improved
• Quadratic forms and Class groups

Residue Class Rings

• Multiplicative and additive groups

Univariate Polynomial Rings

• Improved GCD over Z (GCD-HEU)
• Shoup factorization over large prime finite fields