The Wolfram Language's symbolic character allows it to provide deep integrated support for algebraic numbers. At the core are Root objects, which provide exact implicit representations for arbitrary algebraic numbers. Using specially developed algorithms, the Wolfram Language efficiently handles Root objects just as it does ordinary explicit representations of numbers.

Root — symbolic representation for the root of a polynomial

N — numerical approximation to any precision

MinimalPolynomial — the minimal polynomial for which a number is a root

IsolatingInterval — exact isolating interval for an algebraic number

RootReduce — attempt to reduce to a single Root object

ToRadicals — convert to explicit radicals, if possible

Algebraics — the domain of algebraic numbers, for FullSimplify etc.

RootApproximant — find an algebraic number that approximates a given number

ContinuedFraction — nonperiodic and periodic continued fractions

QuadraticIrrationalQ  ▪  Convergents  ▪  ...

Algebraic Number Theory »

AlgebraicNumber — algebraic number represented in a particular field

ToNumberField — express numbers in a particular algebraic number field