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Introduction
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MAGMA
Summary of New Features in Magma V2.19
December 2012
Introduction
Highlights
Documentation
Language and System Features
Aggregates and Mappings
Algebraic Geometry
Schemes
Sheaves
Algebraic Curves
Algebraic Surfaces
Toric Varieties
Arithmetic Geometry
Rational Curves and Conics
Elliptic Curves
Elliptic Curves over the Rational Field
Elliptic Curves over Finite Fields
Elliptic Curves over Function Fields
Hyperelliptic Curves
L-Series
Brandt Modules
Modular Forms
Modular Symbols
Admissible Representations
Arithmetic Fields (Global)
Algebraic Number Fields
Characters and Artin Representations
Algebraic Function Fields
Arithmetic Fields (Local)
p
-adic Rings and their Extensions
Series Rings
Basic Rings and Fields
Integer Ring
Finite Fields
Nearfields
Real and Complex Fields
Polynomial Rings
Coding Theory
General Linear Codes
Linear Codes over Finite Fields
Linear Codes over Finite Rings
Quantum Error-Correcting Codes
Combinatorial Theory
Graphs
Matrices
Commutative Algebra
Polynomial Rings
Ideal Theory and Gröbner Bases
Geometry
Convex Polytopes and Polyhedra
Finite Geometry
Incidence Geometry
Groups
Automatic Groups
Classical Groups
Finitely Presented Groups
Matrix Groups
Matrix Groups Over Associative Algebras
Matrix Groups Over Finite Fields
Matrix Groups Over
Z
and
Q
Permutation Groups
Quasisimple Groups
Soluble Groups
Lattices
Lattices
Lie Theory
Lie Algebras
Representation Theory
Linear Algebra and Module Theory
Matrices
Sparse Matrices
Bilinear and Sesquilinear Forms
Linear Associative Algebras
Associative Algebras
Basic Algebras
Matrix Algebras
Quaternion Algebras
