Root[f, k] represents the exact k\[Null]^th root of the polynomial equation f[x] == 0. Root[{f, x_0}] represents the exact root of the general equation f[x] == 0 near x = ...

Mathematica's symbolic character allows it to provide deep integrated support for algebraic numbers. At the core are Root objects, which provide exact implicit ...

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

AlgebraicIntegerQ[a] yields True if a is an algebraic integer, and yields False otherwise.

FindRoot[f, {x, x_0}] searches for a numerical root of f, starting from the point x = x_0.FindRoot[lhs == rhs, {x, x_0}] searches for a numerical solution to the equation lhs ...

AlgebraicNumberDenominator[a] gives the smallest positive integer n such that n a is an algebraic integer.

With its convenient symbolic representation of algebraic numbers, Mathematica's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one ...

AlgebraicNumber[\[Theta], {c_0, c_1, ..., c_n}] represents the algebraic number in the field \[DoubleStruckCapitalQ][\[Theta]] given by c_0 + c_1 \[Theta] + ... + c_n ...

AlgebraicNumberTrace[a] gives the trace of the algebraic number a.

RootApproximant[x] converts the number x to one of the "simplest" algebraic numbers that approximates it well.RootApproximant[x, n] finds an algebraic number of degree at ...