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Oscar.jl
  • Welcome to Oscar
    • Architecture
    • Notes for users of other computer algebra systems
    • Frequently Asked Questions
    • Serialization
    • 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
    • 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
      • Saving and loading
      • Visualization
    • Cones
    • Polyhedral Fans
    • Polyhedral Complexes
    • Linear Programs
    • Subdivisions of Points
    • Introduction
    • Creating Multivariate Rings
    • Ideals in Multivariate Rings
      • Introduction
      • Free Modules
      • Subquotient Modules
      • Operations on Modules
    • Affine Algebras
    • Binomial Primary Decomposition
    • Localization
    • Localizations of modules over computable rings
    • Introduction
    • Invariants of Finite Groups
    • Invariants of Linearly Reductive Groups
    • Introduction
      • Rational Parametrizations of Rational Plane Curves
      • Introduction
      • Normal Toric Varieties
      • Cyclic Quotient Singularities
      • Toric Divisors
      • Toric Divisor Classes
      • Toric Line Bundles
      • Line bundle cohomology with cohomCalg
      • Cohomology Classes
      • Algebraic Cycles
      • General schemes
      • Introduction
      • Curves
    • Introduction
      • Introduction
      • Creating PBW-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
    • Documenting 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)
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