Global Fields
Defining number fields, elements, and embeddings.
Quadratic field creation, structure, and element operations.
Cyclotomic field creation, structure, and element operations.
Orders in number fields: creation, arithmetic, and printing.
Automorphism groups, Galois groups, subfields, and cohomology.
Abelian extensions, ray class fields, and Galois module structure.
Étale algebra construction, attributes, and homomorphisms.
Dirichlet and Hecke character construction and properties.
Algebraically closed field representation, structure, and creation.
Rational function field creation, operations, and elements.
Algebraic function field creation and structural invariants.
Class groups, abelian extensions, and Witt rings for function fields.
Artin representation functions, invariants, and arithmetic.