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Algebraic Numbers and Number Fields

Version 10.10 Reference Manual

Home - Algebraic Numbers and Number Fields

Number fields
Base class of number fields
Relative number fields
Splitting fields of polynomials over number fields
Galois groups of number fields
Galois groups of field extensions.
Galois groups of field extensions as permutation groups

Elements of number fields (implemented using NTL)
Number field elements (abstract base class)
Elements optimized for quadratic number fields
Elements of bounded height in number fields

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 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
Universal cyclotomic field

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

Index – _

_GaloisMixin (class in sage.groups.galois_group)
_richcmp_() (sage.rings.qqbar.AlgebraicNumber method)
- (sage.rings.qqbar.AlgebraicReal method)
_SubGaloisMixin (class in sage.groups.galois_group)

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