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Algebraic Numbers
Mathematica'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, Mathematica 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 non-periodic and periodic continued fractions
AlgebraicNumber algebraic number represented in a particular field
ToNumberField express numbers in a particular algebraic number field
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