What can Magma compute?

The Magma Language Sets, Sequences and Mappings Basic Rings Matrices and Linear Algebra Lattices and Quadratic Forms Global Fields Local Fields Modules Finite Groups Finitely Presented Groups Algebras Representation Theory Lie Theory Commutative Algebra Algebraic Geometry Arithmetic Geometry Modular Arithmetic Geometry Topology Geometry Combinatorics Coding Theory Cryptography Optimization