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Introduction

Number Fields

Introduction

Number field operations

Elements

Complex embeddings

p-rationality

Class field theory

Internals

Orders in Number Fields

Introduction

Basics

Elements

Ideals

Fractional ideals

Quadratic and Hermitian Forms

Introduction

Basics

Lattices

Integer lattices

Genera for hermitian lattices

Genera for integer lattices

Discriminant groups

Associative Algebras

Introduction

Basics

Structure constant algebras

Group algebras

Quaternion algebras

Ideals in algebras

Elliptic Curves

Introduction

Basics

Finite fields

Number fields

Abelian Groups

Introduction

Elements

Operations

Morphisms

Finite rings

Introduction

Basic

Ideals

Miscellaneous

Elementary number theory

Factored elements

Sparse linear algebra

Conjugacy of integer matrices

Multisets

Pseudo-matrices

Embedded modules

For Developers

Introduction

Tests

Documentation

References

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Introduction

A finite ring will is represented as an abelian group $A$ together with a $Z$ -bilinear map $A \times A \to A$ encoding the multiplicative structure.

The type for finite rings is FiniteRing and the type for the elements is FiniteRingElem.

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Introduction