Algebraic Numbers and Number Fields

Algebraic Number Fields

• Number Fields
• Base class for all number fields
• Relative Number Fields
• Number Field Elements
• Optimized Quadratic Number Field Elements
• Splitting fields of polynomials over number fields
• Galois Groups of Number Fields
• Elements of bounded height in number fields

Morphisms

• Morphisms between number fields
• Sets of homomorphisms between number fields
• Embeddings into ambient fields
• Structure maps for number fields
• Helper classes for structural embeddings and isomorphisms of number fields

Orders, Ideals, Ideal Classes

• Orders in Number Fields
• Number Field Ideals
• Relative Number Field Ideals
• Class Groups of Number Fields
• Unit and S-unit groups of Number Fields
• Solve S-unit equation x + y = 1
• Small primes of degree one
• \(p\)-Selmer groups of number fields

See also

sage.rings.finite_rings.residue_field

Totally Real Fields

• Enumeration of Primitive Totally Real Fields
• Enumeration of Totally Real Fields: Relative Extensions
• Enumeration of Totally Real Fields
• Enumeration of Totally Real Fields: PHC interface

Algebraic Numbers

• Field of Algebraic Numbers
• Universal cyclotomic field

See also

sage.rings.algebraic_closure_finite_field

Indices and Tables

• Index

• Module Index

• Search Page