Algebraic Number Theory

With its convenient symbolic representation of algebraic numbers, the Wolfram Language's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one of the historically richest areas of pure mathematicsall tightly integrated with the Wolfram Language's powerful unified environment.

ReferenceReference

Algebraic Numbers and Representation »

AlgebraicNumber algebraic number represented in a particular field

Root represent a root of a polynomial

RootApproximant root approximation

IsolatingInterval  ▪  MinimalPolynomial  ▪  AlgebraicNumberPolynomial  ▪  ...

AlgebraicIntegerQ  ▪  AlgebraicUnitQ  ▪  RootOfUnityQ

AlgebraicNumberNorm  ▪  AlgebraicNumberTrace  ▪  AlgebraicNumberDenominator

Algebraic Number Fields

ToNumberField find a common field, or express numbers in a given field

NumberFieldIntegralBasis  ▪  NumberFieldClassNumber  ▪  NumberFieldDiscriminant

NumberFieldRegulator  ▪  NumberFieldSignature

NumberFieldNormRepresentatives  ▪  NumberFieldFundamentalUnits  ▪  NumberFieldRootsOfUnity

Factorization

FactorInteger factorization of integers

Factor factorization of polynomials

GaussianIntegers allow factorization over Gaussian integers

Extension field extension for number theoretic and polynomial operations

RootReduce reduce an algebraic number to minimal Root form

ToRadicals convert to explicit radicals