Algebraic Numbers and Number Fields

Number Fields

• Number fields
• Base class of number fields
• Relative number fields
• Splitting fields of polynomials over number fields
• Galois groups of number fields

Elements

• Elements of number fields (implemented using NTL)
• Elements optimized for quadratic 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 and Ideal Classes

• Orders in number fields
• Ideals of number fields
• Ideals of relative number fields
• Ideals of (Not Necessarily Maximal) Orders in Number Fields
• Class groups of number fields
• Units and \(S\)-unit groups of number fields
• Solver for the \(S\)-unit equation \(x + y = 1\)
• Small primes of degree one
• \(p\)-Selmer groups of number fields

Algebraic Numbers

• Algebraic numbers
• Universal cyclotomic field

Enumeration of Totally Real Fields

• Enumeration of primitive totally real fields
• Enumeration of totally real fields: relative extensions
• Enumeration of totally real fields: data
• Enumeration of totally real fields: PHC interface

Indices and Tables

• Index

• Module Index

• Search Page