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Summary of New Features in Magma V2.15

December 2008

Introduction
Summary
Documentation
Language and System Features
Aggregates
- Sequences
- Multisets
Basic Rings
- Integer Ring
- Multivariate Polynomial Rings
- Finite Fields
Linear Algebra and Module Theory
- Matrices
- Modules over Dedekind domains
Lattices and Quadratic Forms
- Minima and Vector Enumeration
- Attributes of Lattices
Global Arithmetic Fields
- Algebraic Number Fields
- Algebraic Function Fields
- Abelian Extensions
- Artin Representations
Local Arithmetic Fields
- Local Fields
- Local Fields defined by Arbitrary Polynomials (New)
- Algebraic Power Series
- Newton Polygons
Groups
- Finitely Presented Groups
- Finite Groups
- Permutation Groups
- Matrix Groups Over General Rings
- Matrix Groups over Finite Fields
- Almost Simple Groups
- Finite Soluble Groups
- Databases of Groups
- Straight Line Program Groups
Algebras
- Associative Algebras
- Exterior Algebras (New)
- Basic Algebras
- Characters of Finite Groups
Lie Theory
- Coxeter Groups as FP Groups
Commutative Algebra
- Ideal Theory and Gröbner Bases
- Modules over Multivariate Rings
- Invariant Theory
Algebraic Geometry
- Schemes
- Algebraic Curves
- Algebraic Surfaces
Arithmetic Geometry
- Rational Curves and Conics
- Elliptic Curves
- Genus One Models
- Hyperelliptic Curves
  - Hyperelliptic Curves over Finite Fields
  - Hyperelliptic Curves over the Rationals
- L-Functions
Modular Arithmetic Geometry
- Hilbert Modular Forms (New)
- Arithmetic Fuchsian Groups and Shimura Curves
Geometry
- Incidence Geometry
Incidence Structures
- Designs
Coding Theory
- Linear Codes over Finite Fields
- Quantum Stabilizer Codes