Oscar.jl logo
Oscar.jl
  • Welcome to OSCAR
    • Architecture
    • Notes for users of other computer algebra systems
    • Frequently Asked Questions
    • Serialization
    • Complex Algorithms in OSCAR
    • Introduction
    • Basics
    • Subgroups
    • Quotients
    • Products of groups
    • Permutation groups
    • Finitely presented groups
    • Polycyclic groups
    • Matrix groups
    • Group Actions
    • Group homomorphisms
    • Groups of automorphisms
    • Group libraries
    • Abelian Groups
    • Group characters
    • Introduction
    • Ring functionality
    • Integers
      • Univariate polynomial functionality
      • Sparse distributed multivariate polynomials
      • Power series
      • Generic Puiseux series
      • Power series and Laurent series
      • Puiseux series
    • Introduction
    • Field functionality
    • Rationals
    • Factored Elements
    • Class Field Theory
    • Generic fraction fields
      • Padics
      • Qadics
    • Finite fields
    • Introduction
    • Sparse linear algebra
    • Matrix functionality
    • Generic matrix algebras
      • Finitely presented modules
      • Free Modules and Vector Spaces
      • Submodules
      • Quotient modules
      • Direct Sums
      • Module Homomorphisms
      • Introduction
      • Spaces
      • Lattices
      • Genera for hermitian lattices
      • Integer Lattices
      • Genera of Integer Lattices
      • Discriminant Groups
    • Introduction
      • Introduction
      • Number field operations
      • Element operations
      • Internals
      • Introduction
      • Orders
      • Elements
      • Ideals
      • Fractional ideals
    • Abelian closure of the rationals
    • Galois Theory
    • Introduction
      • Introduction
      • Constructions
      • Polyhedron and polymake's Polytope
      • Auxiliary functions
    • Cones
    • Polyhedral Fans
    • Polyhedral Complexes
    • Linear Programs
    • Mixed Integer Linear Programs
    • Subdivisions of Points
    • Introduction
    • Creating Multivariate Rings
    • Ideals in Multivariate Rings
    • Affine Algebras and Their Ideals
    • Localized Rings and Their Ideals
      • Introduction
      • Free Modules
      • Subquotients
      • Operations on Modules
      • Operations on Module Maps
      • Chain and Cochain Complexes
      • Homological Algebra
      • Monomial Orderings
      • Gröbner/Standard Bases Over Fields
      • Gröbner/Standard Bases Over $\mathbb Z$
      • Binomial Primary Decomposition
      • A Framework for Localizing Rings
      • Localizations of modules over computable rings
    • Introduction
    • Invariants of Finite Groups
    • Invariants of Linearly Reductive Groups
    • Introduction
      • General schemes
      • Affine schemes
      • Morphisms of affine schemes
      • Architecture of affine schemes
      • Covered schemes
      • Coverings
      • Introduction
      • Normal Toric Varieties
      • Cyclic Quotient Singularities
      • Toric Divisors
      • Toric Divisor Classes
      • Toric Line Bundles
      • Line bundle cohomology with cohomCalg
      • Cohomology Classes
      • Subvarieties
      • The Chow ring
      • ToricMorphisms
      • Introduction
      • Affine Toric Schemes
      • Normal Toric Schemes
      • Introduction
      • Curves
      • Rational Parametrizations of Rational Plane Curves
      • Standard Constructions in Algebraic Geometry
      • Algebraic Surfaces
    • Introduction
      • Introduction
      • Creating PBW-Algebras
      • Ideals in PBW-algebras
      • GR-Algebras: Quotients of PBW-Algebras
    • Free Associative Algebras
    • Graphs
    • Matroids
    • Simplicial Complexes
    • Introduction
    • GAP's SLPs
    • AbstractAlgebra's polynomial interface
  • References
  • Index
    • Introduction for new developers
    • Developer Style Guide
    • Design Decisions
    • Documenting OSCAR code
    • Debugging OSCAR Code
    • Serialization
      • AbstractCollection
      • SubObjectIterator
Version
  • Number Theory
  • Introduction
  • Introduction
Edit on GitHub
  • Introduction

Introduction

The number theory part of OSCAR provides functionality for algebraic number theory.

It is under development with regard to providing both the functionality and the documentation.

General textbooks offering details on theory and algorithms include:

  • Henri Cohen (1993)
  • Henri Cohen (2000)
  • Daniel A. Marcus (2018)
  • M. Pohst, H. Zassenhaus (1997)
« Discriminant GroupsIntroduction »

Powered by Documenter.jl and the Julia Programming Language.

Settings


This document was generated with Documenter.jl version 0.27.24 on Monday 20 February 2023. Using Julia version 1.6.7.