Magma Handbook
About Magma and the handbook
Syntax, types, control flow, procedures, functions, and the Magma programming model.
Fundamental aggregate types: sets, multisets, sequences, tuples, and mappings.
Integers, rationals, finite fields, residue class rings, and polynomial rings.
Matrix construction, arithmetic, decompositions, and solving linear systems.
Integral lattices, quadratic forms, reduction algorithms, and enumeration.
Number fields and function fields: rings of integers, ideals, class groups, and units.
p-adic fields and formal power series: completions, extensions, and Newton polygons.
Modules over rings, free and finitely generated modules, and homological constructions.
Permutation groups, matrix groups, and generic finite groups with structural algorithms.
Groups given by generators and relations, coset enumeration, and rewriting systems.
Associative and non-associative algebras, quaternion algebras, and crossed products.
Characters, modules over group algebras, and ordinary and modular representations.
Lie algebras, root systems, Coxeter groups, and Chevalley groups.
Ideals in polynomial rings, Gröbner bases, primary decomposition, and schemes.
Schemes, varieties, divisors, and sheaves over general fields.
Elliptic and hyperelliptic curves, Jacobians, rational points, and descent.
Modular forms, modular curves, and related L-functions.
Simplicial complexes, homology groups, and topological invariants.
Projective and affine geometry, polytopes, and incidence structures.
Graphs, designs, permutation groups on sets, and combinatorial enumeration.
Linear codes, decoding algorithms, bounds on minimum distance, and pseudo-random bit sequences.
Integer programming, lattice problems, and optimization over algebraic structures.
Alphabetical index of all functions
Bibliography